Question 1

A fitness chain is considering licensing a proprietary diet. They want to test if the renewal rate for the Atkins diet is more than 4% higher than the conventional diet. Which of the following is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$H_0$$: p_A - p_C \leq 0.04$$ and H_A$$: p_A - p_C \u003e 0.04$$

Question 2

What is the main purpose of randomization in a comparative study between two treatments?

Accepted Answer

To eliminate confounding by balancing unknown factors across groups

Question 3

Given the following 95% confidence intervals for renewal rates: Atkins diet $$(0.648, 0.792)$$ and Conventional diet $$(0.535, 0.665)$$, what can you conclude?

Accepted Answer

The confidence intervals do not overlap, indicating a statistically significant difference

Question 4

If the 95% confidence interval for $$p_A - p_C is$$ $$(0.023, 0.217)$$, what does this imply about the difference in renewal rates?

Accepted Answer

The difference is statistically significant because the interval does not include zero

Question 5

Which of the following best describes confounding in the context of comparing two diets?

Accepted Answer

Confounding is the mixing of effects from two or more factors, making it difficult to isolate the effect of the diet

Question 6

A two-sample t-test is used to compare the mean prices of used four-wheel drive and two-wheel drive luxury cars. Which of the following is the correct null hypothesis if you want to test if four-wheel drive cars command a higher price?

Accepted Answer

$$H_0$$: \$$mu_1$$ - \$$mu_2$$ \leq 0$$

Question 7

Which of the following is NOT a requirement for conducting a two-sample t-test?

Accepted Answer

Samples must have equal variances

Question 8

In a matched pairs t-test comparing sales in 2015 and 2016, the 95% confidence interval for the mean difference is $$(-27.85, -9.84). $$What does this indicate?

Accepted Answer

Sales in 2016 were statistically significantly lower than in 2015

Question 9

Which JMP menu path would you use to conduct a matched pairs t-test for two columns of sales data?

Accepted Answer

Analyze \u003e Specialized Modeling \u003e Matched Pairs

Question 10

If the p-value for a two-sample t-test is 0.0023, what is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

Reject the null hypothesis; there is a statistically significant difference

Question 11

Which formula would you use to calculate the standard error for the difference in proportions between two independent samples?

Accepted Answer

$$\sqrt{\frac{p_1$(1-p_1$)}{n_1$} + \frac{p_2$(1-p_2$)}{n_2$}}$$

Question 12

A business wants to know if a new training program increases employee retention. They compare retention rates between employees who took the program and those who did not. Which statistical test is most appropriate?

Accepted Answer

Two-sample test for proportions

Question 13

Which of the following statements is TRUE about confidence intervals for the difference between two means?

Accepted Answer

If the interval does not contain zero, the difference is statistically significant

Question 14

In the context of business statistics, what does a Type I error represent when comparing two population means?

Accepted Answer

Rejecting a true null hypothesis

Question 15

A company tests if a new product increases average sales. The null hypothesis is $$H_0$$: \mu_{new} - \mu_{old} \leq 0$$. The 95% confidence interval for the difference is (2.5$$, 10.3)$$. What should the company conclude?

Accepted Answer

The new product increases sales by a statistically significant amount

Question 16

Which of the following is a potential consequence of not randomizing subjects in a comparative study?

Accepted Answer

Increased risk of confounding

Question 17

When conducting a two-sample t-test, which condition must be checked regarding the variances of the two samples?

Accepted Answer

The variances must be similar, but the test allows for differences

Question 18

A 95% confidence interval for the difference in means is $$(618.83, 2779.51). $$What does this interval suggest?

Accepted Answer

The difference in means is statistically significant

Question 19

Which of the following best describes the meaning of a p-value in hypothesis testing?

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true

Chapter 17: Comparison – Statistical Methods for Comparing Groups

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