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This third course in the specialisation “Business Statistics and Analysis” introduces confidence intervals and hypothesis testing. First, we conceptualise these tools’ business use. We introduce several computations to create confidence intervals and conduct Hypothesis Tests. Simple apps do this.

Students need Windows Excel 2010 or later to complete course tasks. Some Excel features taught in this course won’t work in prior versions of Excel (2007 and earlier).

Course Apply Link – Business Applications of Hypothesis Testing and Confidence Interval Estimation

#### Quiz 1: Practice Quiz

Q1. As the degrees of freedom increase,

• the t-distribution becomes closer to the standard normal distribution.
• the t-distribution becomes farther from the standard normal distribution.

Q2. For a t-distribution with 10 degrees of freedom, to calculate the probability to the left of the number 2, what Excel function formula should be used?

• =T.DIST(2, 10, FALSE)
• =T.DIST(2, 10, TRUE)
• =1-T.DIST(2, 10, TRUE)
• =1-T.DIST(2, 10, FALSE)

#### Quiz 2: Practice Quiz

Q1. Which of the pictures shows the point that would be calculated with the formula “=T.INV(.10, 10)”?

• B
• A

Q2. We have a t-distribution with 10 degrees of freedom and want to find the point that cuts off a probability of 0.4 to the right. Which of the following formulas would work? Please mark ALL correct responses.

• =T.INV(0.6,10)
• = -T.INV(0.4,10)
• =T.INV(0.4,10)
• = -T.INV(0.6,10)

#### Quiz 3: Practice Quiz

Q1. A confidence
interval for the population proportion is calculated to be [35.6%, 44.4%],
which of the following statements are true? Please mark ALL correct responses.

• The margin of error is 4.4%.
• The actual population proportion must lie between 35.6% and 44.4%.
• We are 98% confident the population proportion falls in this interval.
• 35.6% is the lower limit of the confidence interval.

Q2. When calculating confidence intervals, should the population mean or the mean of the random sample be used? What is the symbol used?

• The population mean, μ
• The mean of the random sample, x̄

#### Quiz 4: Practice Quiz

Q1. For which of the following situations would the use of a confidence interval be appropriate? Please mark ALL correct responses.

• Hypothesizing the color of a random crayon pulled from a box
• Predicting the score earned on a particularly difficult exam
• Estimating the average age of fans at a concert
• Calculating the value of a single unknown variable from an equation

Q2. A confidence interval can be constructed for which of the following entities? Please select ALL correct responses.

• population proportion
• sample mean
• population mean
• population range

#### Quiz 5: Practice Quiz

Q1. When is the t-statistic appropriate to use over the z-statistic? Please select ALL correct responses.

• When the sample standard deviation is unknown but the population standard deviation is known
• When the population standard deviation is unknown but the sample standard deviation is known
• When the population mean and standard deviation are both known
• When the sample size is too large for a z-statistic to handle

Q2. Suppose we are trying to estimate the average annual salary of all high school teachers in a particular region. After gathering data on 100 teachers, we have determined the sample mean to be \$50,000 and the sample standard deviation to be \$5,000. What is the t-statistic associated with this sample if information from the government reveals that the actual average salary (the population mean salary) is \$49,000?

`Enter answer here`

#### Quiz 6: Practice Quiz

Q1. Suppose that the 95% confidence interval for the average height of high school females calculated from a given set of data is [157 < μ < 173] in centimeters. Which of the following could represent a confidence interval (calculated from the same data) at greater than 95% confidence?

• [151 < μ < 167]
• [155 < μ < 175]
• [153 < μ < 181]
• [159 < μ < 171]

Q2. What is the margin of error for the 95% confidence interval of [157 < μ < 173] from above?

`Enter answer here`

#### Quiz 7: Confidence Interval – Introduction

Q1. Suppose we have a t-distribution symmetrically dispersed
around mean of 0, with degrees of freedom 10.

What is the probability that a random value from this distribution will be
greater than 1? Round to 2 decimal places.

`Enter answer here`

Q2. Similarly, what is the probability that the value will fall between -1 and 1? Round to two decimals.

`Enter answer here`

Q3. In the t-distribution with 10 degrees of freedom given above, what is the correct formula to calculate the value that cuts of a probability of 10% to the left of that value?

• =1-T.INV(10, .10)
• =T.DIST(.10, 10)
• =T.INV(.10, 10)
• =1-T.DIST(10, .10)

This spreadsheet shows how a sample of portfolio managers fared on the stock market for the previous year. The numbers are in ‘percentage’, for example a stock return of 23.22 implies that the stock return was 23.22%. Each number represents a manager’s most recent annual return.

Construct a histogram with an appropriate bin size to visualize the data. How are the returns distributed? Choose the most appropriate option from the following.

• Skewed to the right
• Normal distribution
• Skewed to the left
• Uniform distribution

Q5. What is the average return for the sample of portfolio managers in the data? For the rest of the quiz, provide your answer rounded to two decimal places.

`Enter answer here`

Q6. What is the sample standard deviation of return for the portfolio managers?Provide your answer rounded to two decimal places.

`Enter answer here`

Q7. Suppose we know that the actual population standard deviation is 9 (i.e. 9%). We wish to construct a confidence interval for the average return for the population of portfolio managers. Use the value of zα/2 to be 2. What is the resulting confidence interval?

HINT: Please use the formula for confidence interval of a population mean using the z-statistic.

• [1.24%, 8.68%]
• [0.40%, 9.52%]
• [4.04%, 5.48%]
• [1.12%, 8.40%]

Q8. How many portfolio returns in the data lie within this confidence interval?

HINT: you can either use the COUNTIF function or sort the data and then manually count the observations

• 29
• 34
• 46
• 55

#### Quiz 1: Practice Quiz

Q1. If given an alpha (α) of 0.10, what is the corresponding confidence interval percentage?

• 80%
• 90%
• 10%
• 20%

Q2. If
given a sample standard deviation, what formula should be used to calculate the
confidence interval for the unknown population mean?

• =x̄ ± |Zα/2 |* σ/√n
• =x̄ ±
|tα/2 |* s/√n
• =CONFIDENCE.T(α,
s, n)
• =CONFIDENCE.NORM(α, σ, n)

#### Quiz 2: Practice Quiz

Q1. When calculating the confidence interval for a population proportion, what should one use?

• z-statistic
• Both the z-statistic and the t-statistic
• t-statistic
• Neither the z-statistic nor the t-statistic

Q2. Which of the following represents a sample proportion?

• p
• s
• σ

#### Quiz 3: Practice Quiz

Q1. Which of the following should one take into consideration when determining how big a sample to take? Please mark ALL correct responses.

• Population Mean
• Margin of Error
• Confidence Level
• Population Proportion
• Reasonable Approximation of Population Standard Deviation

Q2. In calculating an appropriate sample size “n”, your calculations reveal that √n is equal to 7.5. What is the appropriate sample size?

`Enter answer here`

#### Quiz 4: Practice Quiz

Q1. Suppose one is trying to calculate a sample size for a given margin of
error in a population proportion confidence interval. What value should be used
for p̂ if p̂ is unknown?

• 0
• .5
• .95
• 1

Q2. Which of the following is the formula to calculate the sample size n
given a margin of error E for a population proportion?

n = (|zα/2|/E)2

• p̂(1-p̂)

n = (E/|zα/2|)2

• p̂(1-p̂)

n = |zα/2|2 * p̂(1-p̂)/E

n =
|zα/2|2

• E/(p̂(1-p̂))

#### Quiz 5: Practice Quiz

Q1. The steps of a hypothesis test include which of the following? Answer ALL that apply.

• Taking sample data from multiple populations
• Making an assumption or claim
• Gathering more data if n is less than 100
• Testing whether the sample meets the assumption or claim

Q2. A scientific procedure of hypothesis testing takes into account which of the following? Answer All that apply.

• Size of the sample
• Variability in the sample
• Level of significance desired in the conclusion
• Gut feeling on significance of data

#### Quiz 6: Confidence Interval – Applications

This spreadsheet lists last month’s sales for a sample of 100 department stores. The sales are divided into categories of grocery sales, clothing sales, and toy sales.

Suppose we are trying to estimate the average grocery sales for all stores, of which we have data for these 100. Calculate the absolute value of t-α/2 for a 95% confidence interval for grocery sales. Round to four decimal places.

`Enter answer here`

Q2. Using the non-rounded value (full value given by Excel) calculated in question #1, calculate the margin of error for grocery sales. Round your answer to four decimal places.

`Enter answer here`

Q3. Now calculate the margin of error for a 95% confidence interval for the population mean clothing sales and toy sales as well. Which of the three categories has the greatest margin of error?

• Grocery Sales
• Clothing Sales
• Toy Sales

Q4. Suppose we could gather more data points for
clothing sales from additional stores. In order to make the margin of error for
clothing sales as close as possible to the current margin of error for toy sales, how many additional
data points would be required?

Assume that the mean and sample standard
deviation remain the same. Round to the nearest whole number.

`Enter answer here`

Q5. What is the 95% confidence interval for the population mean toy
sales (rounding to the nearest whole number)?

• [9126, 10556]
• [9156, 10526]
• [26067, 30193]
• [8126, 11556]

Q6. Compared to the 95% confidence interval, is the 90% confidence interval for toy sales wider or narrower?

• Narrower; the margin of error for the 90% confidence interval is smaller, leading to a narrower range.
• Wider; the margin of error for the 90% confidence interval is larger, leading to a wider range.

Q7. What is the 90% confidence interval for the population mean toy sales. Round to the nearest whole number.

• [9268, 10414]
• [9156, 11234]
• [10016, 12006]
• [8956, 10024]

Q8. How many more store toy sales fall within the 95%
confidence interval than within the 90% confidence interval?

HINT: Count the number of data points that fall within each interval separately. For counting you could either do a manual count or use the COUNTIF function in Excel. Please refer to course 1 of this specialization where we covered the usage of such functions.

`Enter answer here`

Q9. Complete the following statement by filling in the blanks. More than one answer choice may be correct.

For a given standard deviation, the margin of error as the sample size .”

• decrease; decreases
• increases; decreases
• decreases; increases
• increases; increases

Q10. Now we will work with population proportions. Enter an appropriate formula in column E that will calculate the total sales as the sum of the three categories of sales for each store.

In column F calculate the average proportion of grocery sales relative to total sales per store. That is in column F calculate columnB/columnE.

Report the average of this column (column F). This is your (p̂). Round your answer to two decimal places.

`Enter answer here`

Q11. Construct a 95% confidence interval for the population proportion of grocery sales. [Hint: use the z-statistic]

• [9156, 10526]
• [.3728, .5685]
• [.2617, .6796]
• [31345, 34170]

Q12. Suppose
we could gather more data points for clothing sales from additional stores. In
order to make the margin of error for the population proportion confidence
interval of clothing sales equal to .07, how many additional data points would
be required? Round to the highest whole number.

HINT: Use the z-statistic and remember to use a value of 0.5 for p̂.

`Enter answer here`

#### Quiz 1: Practice Quiz

Q1. Which of the following statements about hypothesis testing are correct? Please mark ALL correct statements.

• If the sample mean falls in the rejection
region, you can reject the claim.
• If the t-statistic does not fall in the rejection region, you can not reject the claim.
• If the t-statistic does not fall in the rejection region, you can reject the claim.
• If the z-statistic falls in the rejection region, you can reject the claim.

Q2. For the Hypothesis Tests we studied, the rejection regions are set so that the probability of rejection in each tail of the distribution is equal to:

• α
• α/2
• σ/√n
• s/√n

#### Quiz 2: Practice Quiz

Q1. The four steps of hypothesis testing are listed below. In which order should they be executed?

A. Check whether t-statistic falls in the rejection region

B. Formulate Hypothesis

C. Calculate the cutoff values for the t-statistic

D. Calculate the t-statistic

• D, B, C, A
• B, D, C, A
• A, B, C, D
• C, B, D, A

Q2. In a two tail test, which of the following correctly completes the sentence? (Please mark ALL correct responses)

• the absolute value of the t-statistic is greater than the absolute value of the cutoff value.
• the t-statistic falls in the rejection region.
• the t-statistic is smaller than the cutoff value.
• the t-statistic falls outside one standard deviation of the mean.

#### Quiz 3: Practice Quiz

Q1. Please mark ALL correct responses.

• each rejection region has size α/2.
• there are two rejection regions.
• there is one rejection region.
• each rejection region has size α.

Q2. In which of the following scenarios do we reject the null hypothesis for a single tail hypothesis test? Please mark ALL correct responses.

• When the rejection region is on the right and the t-statistic is less than the cutoff value
• When the rejection region is on the right and the t-statistic is greater than the cutoff value
• When the rejection region is on the left and the t-statistic is less than the cutoff value
• When the rejection region is on the left and the t-statistic is greater than the cutoff value

#### Quiz 4: Practice Quiz

Q1. A scientist claims that the average adult sleeps more than 7.5 hours each night. Suppose we have data from a random sample of 100 adults and wish to test this claim using hypothesis testing.

Which of the following would be an appropriate null hypothesis, and on which side would the rejection region lie?

• Null hypothesis: μ > 7.5; rejection region on the right side
• Null hypothesis: μ ≤ 7.5; rejection region on the right side
• Null hypothesis: μ < 7.5; rejection region on the left side
• Null hypothesis: μ ≥ 7.5; rejection region on the left side

Q2. Using the information in question 1, what is the t-cutoff value? Assume an α value of 0.05. Round your answer to two decimal places.

`Enter answer here`

#### Quiz 5: Practice Quiz

Q1. Which conditions must be satisfied in order to use population proportion hypothesis test? Select ALL that apply.

• p * p_bar > 5
• n * (1 – p_bar) > 5
• n * p > 5
• n * p_bar > 5

Q2. We wish to test a claim that at least 40% of high school students play a musical instrument. Out of 100 randomly-selected students, 35 report to playing a musical instrument. Suppose we use a population proportion hypothesis test. What is the z-statistic corresponding to our sample data? Report your answer to two decimal places.

`Enter answer here`

#### Quiz 6: Practice Quiz

Q1. Type I error occurs when we _ the null hypothesis when it is true. Type II error occurs when we _ the null hypothesis when it is false.

• reject; fail to reject
• reject; reject
• fail to reject; fail to reject
• fail to reject; reject

Q2. In order to decrease the likelihood of Type I error, we can

• decrease the sample size.
• change the null hypothesis.
• increase alpha.
• decrease alpha.

#### Quiz 7: Hypothesis Testing

Q1. Download spreadsheet Airlines Data, which contains a sample data about flight information for three separate airlines. Time delays are measured in minutes, with negative numbers representing flights that arrived early.

Fast Air claims that their flight delays are on average less than or equal to 20 minutes. We will perform an appropriate hypothesis test for this claim. We will assume an alpha of 0.05 for all tests.

First, report the average time delay in minutes for all Fast Air flights. Round your answer to two decimal places.

Q2. What is the appropriate Null and alternate Hypothesis associated with this test?

• H0: µ > 20
• HA: µ ≤ 20
• H0: µ = 20
• HA: µ != 20
• H0: µ ≥ 20
• HA: µ < 20
• H0: µ ≤ 20
• HA: µ > 20

Q3. Find the t-statistic for this hypothesis test. Round your answer to four decimal places.

`Enter answer here`

Q4. Determine the cutoff value for the t-statistic. Round your answer to four decimal places.

`Enter answer here`

Q5. Now compare the t-statistic to the rejection region. What can we conclude about the null hypothesis?

The t-statistic does not fall in the rejection region; therefore we reject the null hypothesis.

The t-statistic falls in the rejection region; therefore we reject the null hypothesis.

The t-statistic does not fall in the rejection region; therefore we fail to reject the null hypothesis.

The t-statistic falls in the rejection region; therefore we fail to reject the null hypothesis.

Q6. Not to be outdone by their competitors, the second airline in the data, EZ Jet, advertises that their average flight delay is less than 20 minutes. We will perform a hypothesis test on this claim.

Notice that EZ Jet uses a strict inequality in its claim. In this case, what is the appropriate null hypothesis?

• H0: µ < 20
• H0: µ ≤ 20
• H0: µ > 20
• H0: µ ≥ 20

Q7. Calculate the mean, standard deviation, and t-statistic for this hypothesis test (the hypothesis test in Question 6). Your t-statistic should be -1.022.

Now calculate and report the cutoff value for the t-statistic using an alpha value of 0.05. Round your answer to four decimal places.

`Enter answer here`

Q8. Do we reject the null hypothesis? Therefore what can be said about EZ Jet’s claim?

• Yes, we reject the null hypothesis; thus EZ Jet’s claim that their wait time is less than 20 minutes can be rejected.
• No, we do not reject the null hypothesis; thus EZ Jet’s claim that their wait time is less than 20 minutes can be rejected.
• No, we do not reject the null hypothesis; thus EZ Jet’s claim that their wait time is less than 20 minutes can be accepted.
• Yes, we reject the null hypothesis; thus EZ Jet’s claim that their wait time is less than 20 minutes can be accepted.

Q9. The third airline in the data, Comfy Flight, claims that at least 80% of their flights are either early, on-time, or delayed by 20 minutes or less. We will perform a hypothesis test on this claim.

First, determine the number of flights that fit the description above and convert this to a sample proportion. Report the sample proportion, rounding the answer to four decimal places.

HINT: You can use the =COUNTIF function in Excel to count the number of flights for Comfy Flight that fit the description then divide that by the total number of flights for Comfy Flight.

`Enter answer here`

Q10. Write down the Null and Alternate Hypothesis associated with this test.

• H0: p = 0.8
• HA: p != 0.8
• H0: p ≥ 0.8
• HA: p < 0.8
• H0: p > 0.8
• HA: p < 0.8
• H0: p > 0.8
• HA: p ≤ 0.8

Q11. Now calculate and report the z-statistic associated with this Hypothesis test (the Hypothesis test in Question 10). Report your answer to four decimal places.

Q12. The cutoff value for the z-statistic is -1.6449. Is Comfy Flight’s claim substantiated?

• No, we reject the null; 80% of their flights do not fall in this range (either early, on-time, or delayed by 20 minutes or less)
• Yes, we accept the null; 80% of their flights do fall in this range (either early, on-time, or delayed by 20 minutes or less)
• No, we accept the null; 80% of their flights do fall in this range (either early, on-time, or delayed by 20 minutes or less)
• Yes, we reject the null; 80% of their flights do not fall in this range (either early, on-time, or delayed by 20 minutes or less)

#### Quiz 1: Practice Quiz

Q1. Suppose we have data from two different populations, such as men and women, but wish to calculate summary statistics on data from only one population. What approach can be used to separate the data before commencing calculations?

• Create a pivot table in Excel
• Use the sort function in Excel
• Use the filter option in Excel

Q2. In the example given in the video, why do we
need to flip the null and alternate hypotheses?

• There is a strict inequality given in the
original null hypothesis
• There is no inequality given in the original
null hypothesis
• We don’t know whether male Olympic athletes will have greater heights than average males
• We know male Olympic athletes will have greater heights than average males

#### Quiz 2: Practice Quiz

Q1. Which of the following statements are true regarding the Difference in Means tests assuming equal variances?

• Typically, assuming either unequal or equal variances across the two populations will yield different conclusions
• The two sample sizes need not be equal
• The two sample sizes need to be equal
• Typically, assuming either unequal or equal variances across the two populations will yield the same conclusion

Q2. When calculating the t-statistic in a Difference
of Means test, what considerations need to be made?

• Realization that the judgment made regarding
variation is objective
• Consideration of whether the variances of the two populations are more similar or dissimilar
• Realization that the judgment made
regarding variation is subjective
• Assumption of either equal or unequal variance
across the two populations

#### Quiz 3: Practice Quiz

Q1. When running the Two Sample T-test through the Data Analysis tool in Excel, assuming equal variances across the two populations, how is Variable 1 determined?

• Whichever µ comes first in the null hypothesis
• Whichever µ comes last in the null hypothesis
• Whatever the null hypothesis is equal to
• Whatever the null hypothesis is not equal to

Q2. How do we access the Difference in Means hypothesis tests in Excel?

• Data tab >>> Sort
• Data tab >>> Solver
• Data tab >>> Data Analysis
• Data tab >>> Filter

#### Quiz 4: Practice Quiz

Q1. In which of the following examples would a
paired t-test NOT be the test most likely to be used?

• Data of individuals’ original grades on the GMAT
and then grades after completing a course to determine whether taking a course
improved their scores
• Data of customer satisfaction ratings for individual retail stores before and after they attended a training
• Data of the before and after weights of individuals to determine if an exercise program is successful
• Data of how many students signed up for a
class and how many completed the class to measure satisfaction rates

Q2. Typically, is the decision between a paired t-test and an equal or unequal variances t-test important?

• The decision is not important; the results will be the same
• The decision is important; the results will be
the same
• The decision is important; the tests may give different t-statistics and different t-cutoffs
• The decision is important; the conclusions
may be reversed in the two types of tests

#### Quiz 5: Practice Quiz

Q1. Differences in Means tests are used to test which of the following?

• Claims about differences in two population means
• Claims about differences in any number of sample means
• Claims about differences in two sample means
• Claims about differences in any number of population means

Q2. Which of the following is NOT likely a business application for a Differences in Means test?

• Comparing satisfaction scores across all sales regions (states in the U.S.)
• Checking if training provided to employees
is actually effective
• Seeing whether customer reviews are better for one product or for another product
• Testing a claim about sales figures in two
different regions

#### Quiz 6: Practice Quiz

Q1. Suppose we have GMAT scores for male and female MBA
applicants. We want to test whether the average GMAT score for male applicants
is greater than or equal to the average score for female applicants. We calculate the t-statistic (the t-score) and cutoff point and find that the t-statistic falls in the rejection region. What is our conclusion?

• We fail to reject the null hypothesis; the difference between the average GMAT scores for male and female candidates is not greater than or equal to zero
• We reject the null hypothesis; the difference between the average GMAT scores for male and female candidates is not greater than or equal to zero
• We reject the null hypothesis; the difference
between the average GMAT scores for male and female candidates is greater than or
equal to zero
• We fail to reject the null hypothesis; the
difference between average GMAT scores for male and female candidates is
greater than or equal to zero

Q2. What does the conclusion imply?

• We accept the alternate hypothesis; the difference between the average GMAT scores for male and female candidates is less than zero
• We reject the alternate hypothesis; the difference between the average GMAT scores for male and female candidates is less than zero
• We reject the alternate hypothesis; the difference between the average GMAT scores for male and female candidates is greater than zero
• We accept the alternate hypothesis; the difference between the average GMAT scores for male and female candidates is greater than zero

#### Quiz 7: Hypothesis Test – Differences in Mean

This spreadsheet gives a sample of the interns’ scores on a test they took on the first day of their internship, and then after they had completed a training. The company is trying to determine whether it is worth spending money on the training. Do the interns’ scores either remain the same or improve from the training? In other words, we want to test whether the scores after training are at least as high as the scores before the training.

What is the most appropriate test to conduct in Excel?

• Data Analysis, z-test: Two Sample for Means
• t-test: Two-Sample Assuming Equal
Variances
• Data Analysis, t-test: Two-Sample Assuming
Unequal Variances
• t-test: Paired Two Sample
for Means

Q2. Now run the test using the data analysis tool in Excel. Use an alpha level of 0.05. The null and alternate hypothesis for such a test would be as follows,

H0: µ(score after) – µ(score before) ≥ 0

HA: µ(score after) – µ(score before) < 0

decimal places.

`Enter answer here`

Q3. What is the absolute value of the t-statistic cutoff? Round your answer to two decimal places.

`Enter answer here`

Q4. What should be the conclusion?

• We do not reject the null hypothesis; scores after training
are significantly lower than scores before, and thus the training is not
worthwhile.
• We do not reject the null hypothesis; scores after
training are at least as high as scores before, and thus the training is
worthwhile.
• We reject the null hypothesis; scores after
training are at least as high as scores before, and thus the training is
worthwhile.
• We reject the null hypothesis; scores after
training are significantly lower than scores before, and thus the training is
not worthwhile.

Q5. You will notice in the data that the interns’ ages and genders are included as well. The HR manager in charge of hiring the interns wants to see whether the average scores of the female interns are equal to the average scores of the male interns (use the ‘Score After Training’ for the rest of the questions).

What is the average score for the female

`Enter answer here`

Q6. What is the average score for the male interns? Round your answer to two decimal places.

`Enter answer here`

Q7. Suppose we do not know whether the variance in scores for female interns is similar or dissimilar to the variance in scores for male interns. What types of tests are appropriate to use in Excel? Mark ALL options that apply.

• z-test: Two Sample for Means
• t-test: Two-Sample Assuming Equal Variances
• t-test: Paired Two Sample for
Means
• t-test: Two-Sample Assuming Unequal
Variances

Q8. As mentioned earlier, the HR manager in charge of hiring the interns wants to see whether the average scores of the female interns are equal to the average scores of the male interns (using the ‘Score After Training’).

The Null and Alternate hypothesis for such a test would be as follows,

H0: µ(score after, Females) – µ(score after, Males) = 0

HA: µ(score after, Females) – µ(score after, Males) != 0

Now run any test that you picked in question 7 to answer the above question. What is the resulting t-statistic? Round your answer to two decimal places.

`Enter answer here`

Q9. What is the absolute value of the t-statistic cutoff? Please round your answer to two decimal places.

`Enter answer here`

Q10. What should be the conclusion?

• We reject the null hypothesis; average after scores of
male and female interns are the same.
• We do not reject the null hypothesis; average after scores
of male and female interns are not the same.
• We do not reject the null hypothesis; average after scores of
male and female interns are the same.
• We reject the null hypothesis; the average after scores of male and female interns are not the same

#### Course Content:

WEEK 1

Module 1: Confidence Interval – Introduction
This session explains a confidence interval’s idea and construction. We’ll introduce the t-distribution, t-statistic, z-statistic, and associated excel formulas. We’ll utilize these to establish confidence intervals.

• Introducing the t-distribution, T.DIST, and T.INV excel functions • Conceptual understanding of a Confidence Interval • The z-statistic and t-statistic • Constructing a Confidence Interval using z-statistic and t-statistic

WEEK 2: Confidence Interval Applications
This subject explains business applications of the confidence interval, including calculating sample size. We also apply the confidence interval for a population proportion. Near the module’s end, we introduce Hypothesis Testing.

Confidence interval applications, population proportion confidence interval, sample size calculation, and hypothesis testing are presented.

Module 3: Testing Hypotheses
The module introduces Hypothesis Testing. You learn hypothesis-test logic. The four procedures for conducting a hypothesis test are introduced and applied to mean and proportion tests. You’ll learn about single tail and two tail hypothesis testing, Type I and Type II mistakes, and techniques to reduce them.

• The Logic of Hypothesis Testing • The Four Steps for Conducting a Hypothesis Test
• Hypothesis Test Guidelines, Formulas, and Application • Hypothesis Test for Population Proportion

Hypothesis Test – Mean Differences
In this module, you’ll use the difference in means tests to compare two sets of data. We’ll introduce three means to test differences and apply them to business applications. We’ll also introduce Excel’s hypothesis testing dialogue box.

The Equal & Unequal Variance Assumption and Paired t-test for difference in means is discussed.
• Apps

• Data analysis
• Excel Hypothesis Testing

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