Question 1

A fitness chain wants to test if their proprietary diet leads to a higher membership renewal rate than the conventional diet. Let $$p_A be $$the proportion of renewals for the Atkins diet and $$p_C$$ for the conventional diet. Which of the following is the correct null and alternative hypothesis for testing if the Atkins diet is more effective by more than 4%?

Accepted Answer

$$H_0$$: p_A - p_C \leq 0.04$$; H_A$$: 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 proportions: Atkins diet $$[0.648, 0.792]$$, Conventional diet $$[0.535, 0.665]$$, what can you conclude about the difference in renewal rates?

Accepted Answer

There is a statistically significant difference because the intervals do not overlap.

Question 4

If the 95% confidence interval for $$p_A - p_C is$$ $$[0.023, 0.217]$$, what does this imply about the effectiveness of the Atkins diet compared to the conventional diet?

Accepted Answer

The Atkins diet leads to a statistically significantly higher renewal rate.

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

The variances of the two populations must be exactly equal.

Question 8

In a two-sample t-test, the 95% confidence interval for $$\mu_1$ - \mu_2$ is $$[618.83, 2779.51]$$. What does this indicate?

Accepted Answer

The means are statistically significantly different because the interval does not include zero.

Question 9

A retail chain wants to know if sales per square foot changed from 2015 to 2016. The 95% confidence interval for the mean difference is $$[-27.85, -9.84]. $$What is the correct interpretation?

Accepted Answer

Sales decreased significantly from 2015 to 2016.

Question 10

Which JMP menu path would you use to conduct a paired t-test for matched variables such as sales in 2015 and 2016?

Accepted Answer

Analyze \u003e Specialized Modeling \u003e Matched Pairs

Question 11

If you are comparing the mean difference in sales between two years for the same stores, which statistical test is most appropriate?

Accepted Answer

Paired t-test

Question 12

Which of the following statements is TRUE regarding confidence intervals for differences in means or proportions?

Accepted Answer

If the confidence interval does not include zero, the difference is statistically significant.

Question 13

Suppose you are testing $$H_0$$: \$$mu_1$$ - \$$mu_2$$ \leq 0$$ vs H_A$$: \$$mu_1$$ - \$$mu_2$$ \u003e 0$$ and obtain a p-value of 0.0023. What is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

Reject $$H_0$$; there is significant evidence that $$\mu_1$ \u003e \mu_2$.

Question 14

Which of the following best describes the meaning of a 95% confidence interval for a difference in means?

Accepted Answer

If we repeated the study many times, about 95% of the calculated intervals would contain the true difference.

Question 15

A company wants to know if a new training program increases employee productivity. They randomly assign employees to either the new or old program and compare average productivity. Which statistical method should they use?

Accepted Answer

Two-sample t-test

Question 16

Which of the following is a potential consequence of not randomizing when comparing two treatments?

Accepted Answer

Confounding, making it difficult to attribute differences to the treatments

Chapter 17: Comparison – Statistical Methods for Comparing Groups

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