Question 1

A human resources department is comparing two employee training programs to see if they lead to different pass rates on a required certification program. In Program A, 16 out of 20 employees passed the exam. In Program B, 30 out of 40 employees passed. Are the basic conditions met to conduct a 2-proportion hypothesis test?

Accepted Answer

Yes, the basic conditions are met

Question 2

A school administrator wants to compare the proportion of students who passed a standardized math exam in two different schools by taking samples from 2 classes. Class A: 72 out of 120 students passed. Class B: 65 out of 100 students passed. Calculate the $$z-$$score for testing whether there is a significant difference in the population proportions of student passing rates. (Do not find a $$P-$$value or draw a conclusion.)

Accepted Answer

$$z = \frac{0.6 - 0.65}{\sqrt{0.625 \cdot 0.375 \left( \frac{1}{120} + \frac{1}{100} \right)}}$$

Question 3

A study on the effectiveness of seatbelts in reducing injuries is done using two random samples of drivers. Among the group who were not wearing their seatbelt, 50 drivers were injured and 2350 were not. Among the group who were wearing a seatbelt, 15 were injured and 1585 were not. Use a 0.01 significance level to test the claim that not wearing a seatbelt results in a greater proportion of injuries. What is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$, $$H_a: p_1$ \u003e p_2$

Question 4

A researcher constructs a 90% confidence interval for the difference in two proportions and calculates $$p_1$$ - $$p_2 = 0.09$ with a margin of error of 0.07. Should they reject or fail to reject the claim that there is no difference in these two proportions?

Accepted Answer

Reject

Question 5

A university wants to know if students who live on campus are more likely to attend campus events than students who live off campus. In a sample of 150 on-campus students, 102 attended at least one campus event in the past month. In a sample of 130 off-campus students, 74 attended at least one campus event in the past month. Construct a 95% confidence interval for the difference in proportion. Which formula should be used for the margin of error?

Accepted Answer

$$E = z_{\alpha/2} \cdot \sqrt{\frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1$} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2$}}$$

Question 6

A company is looking to outsource communications to a call center and is trying to decide between two options. They find that 476 of 500 customers are satisfied for Center A and 623 out of 700 are satisfied for Center B. They are interested in seeing if there is enough evidence to suggest that the proportion of satisfied customers is higher for Center A. Which test should be used?

Accepted Answer

Two-proportion $$z-$$test

Question 7

Researchers are comparing the average number of hours worked per week by employees at two different companies. Company A: $$n_1 = 25$, $$\bar{x}_1 = 22.4$$, s_1$ = 3.2. $$Company B: $$n_2 = 16$, $$\bar{x}_2 = 21.1$$, s_2$ = 2.9. $$Assuming population standard deviations are unknown and unequal, calculate the $$t-$$score for the difference in means.

Accepted Answer

$$t = \frac{22.4 - 21.1}{\sqrt{\frac{3.2^2$}{25} + \frac{2.9^2$}{16}}}$$

Question 8

A school claims a new math app will improve test scores. They have 2 independent, random samples of 50 students, one using the traditional method ($$\bar{x}_1 = 77$$, $$s_1 = 4.8$) and the other using the new app ($$\bar{x}_2 = 82$$, s_2$ = 4.4). $$The school assumes the population variances are equal. What is the correct formula for the pooled standard deviation?

Accepted Answer

$$s_p^2$ = \frac{(n_1$ - 1)s_1$^2 + (n_2$ - 1)s_2$^2}{(n_1$ - 1) + (n_2$ - 1)}$$

Question 9

A grocery chain wants to see if self-checkout lanes have a shorter checkout time than cashier lanes. They take a random, independent sample of 35 times from each and find $$\bar{x}_1 = 4.5$$, $$\bar{x}_2 = 6.4$$, $$\$$sigma_1$$ = 1.1$$, $$\$$sigma_2$$ = 1.4. $$What is the correct formula for the $$z-$$score in this hypothesis test?

Accepted Answer

$$z = \frac{4.5 - 6.4}{\sqrt{\frac{1.1^2$}{35} + \frac{1.4^2$}{35}}}$$

Question 10

A personal trainer is studying whether a new stretching routine improves flexibility. She records the forward reach (in cm) of 6 clients before and after a 4-week program. Which type of statistical test should be used to analyze the mean difference?

Accepted Answer

Matched pairs $$t-$$test

Question 11

A company claims its new medication reduces blood pressure. In a study, the sample mean difference in 37 patients’ blood pressure before and 15 days after taking the medication was 3.2 with a standard deviation of 6.7. What is the correct formula for the $$t-$$statistic in this matched pairs test?

Accepted Answer

$$t = \frac{3.2 - 0}{6.7 / \sqrt{37}}$$

Question 12

Which statement about the F-distribution is always true?

Accepted Answer

It is always right-skewed and takes only positive values.

Question 13

In a two-sample Hypothesis Test for Variance, what does an F-statistic near 1 indicate?

Accepted Answer

The two sample variances are approximately equal.

Question 14

A bakery wants more consistent cookies, so they test the weights (in grams) of cookies made in two different ovens. Oven A produced 16 cookies with a standard deviation of 2.45, Oven B produced 11 cookies with a standard deviation of 1.26. What is the correct formula for the F-statistic in this test?

Accepted Answer

$$F = \frac{2.45^2$}{1.26^2$}$$

Question 15

A historian is comparing the variation in weights of rare coins from different time periods. The data from two independent random samples is shown below. Using a 0.05 significance level and a graphing calculator, which function should be used to find the P-value for the F-statistic?

Accepted Answer

Fcdf()

Inferences from Two Samples: Proportions, Means, and Variances

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