Question 1

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Accepted Answer

The null hypothesis typically states there is no difference or effect, so $H_0: \mu_1 - \mu_2 = 0$ is correct. The alternative hypothesis reflects the belief or claim being tested; since the claim is that women take more personal time than men, $H_A: \mu_1 - \mu_2 > 0$ correctly represents this belief.

Question 2

11eb4928_20e4_b11a_b114_571d30050bee_TB7192_00

Accepted Answer

The confidence interval for the difference in proportions is calculated using the formula for two independent proportions. The interval $(-0.279, 0.049)$ correctly reflects the difference between the proportions of freshmen and sophomores who purchased used textbooks, considering the sample sizes and the confidence level.

Question 3

11eb4928_20e4_b11b_b114_0579b7136956_TB7192_00

Accepted Answer

The confidence interval (0.234, 0.421) for $p_s - p_f$ suggests we are 90% confident that the true difference in proportions (sophomores' proportion minus freshmen's proportion) falls within this range, indicating sophomores are between 23.4% and 42.1% more likely to have bought used textbooks compared to freshmen.

Question 4

A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies.If the researcher fails to find a
Significant difference, when in fact one exists in the population:

A)the null hypothesis was correctly accepted.
B)the research hypothesis was correctly accepted.
C)the null hypothesis was correctly rejected.
D)a Type 2 error has been made.
E)a Type 1 error has been made.

Accepted Answer

A Type 2 error occurs when the null hypothesis is not rejected, but it should have been because there is a true effect or difference in the population that the study failed to detect.

Question 5

11eb4928_20e4_8a09_b114_17800ad797e8_TB7192_00

Accepted Answer

The p-value (0.00162) is less than the significance level ($\alpha = 0.05$), indicating strong evidence against the null hypothesis, leading to its rejection.

Question 6

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Accepted Answer

The answer of 11eb4928_20e4_d82e_b114_fb18ad57f7a7_TB7192_00...

Question 7

11eb4928_20e4_d82c_b114_c5586a6535ab_TB7192_00

Accepted Answer

The $P$-value in hypothesis testing represents the probability of observing data as extreme as or more extreme than the observed data, given that the null hypothesis is true. A $P$-value of 0.0147 means there is about a 1.47% chance of seeing the observed difference or larger in the population proportions if there is actually no difference between them.

Question 8

A survey of randomly chosen adults found that 38 of the 61 women and 46 of the 83 men follow regular exercise programs.Construct a 95% confidence interval for the difference in
The proportions of women and men who have regular exercise programs.

A)(-0.124, 0.786)
B)(-0.093, 0.231)
C)(-0.124, 0.815)
D)(0.460, 0.786)
E)(0.430, 0.815)

Accepted Answer

The correct confidence interval for the difference in proportions is calculated using the formula for two independent proportions. The interval (-0.093, 0.231) suggests a small difference between the proportions of women and men who follow regular exercise programs, which is plausible given the provided data.

Question 9

A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies.If the researcher fails to find a
Significant difference, when in fact one exists in the population:

A)the null hypothesis was correctly accepted.
B)the research hypothesis was correctly accepted.
C)the null hypothesis was correctly rejected.
D)a Type 2 error has been made.
E)a Type 1 error has been made.

Accepted Answer

A Type 1 error occurs when the null hypothesis (which states there is no effect or no difference) is incorrectly rejected in favor of the alternative hypothesis, even though the null hypothesis is true. In this scenario, claiming a significant difference between groups when none exists is a classic example of a Type 1 error.

Question 10

11eb4928_20e4_d82d_b114_ad4f4a62813d_TB7192_00

Accepted Answer

The correct interpretation of a confidence interval for the difference between two proportions ($p_w - p_m$) is that we are 90% confident the true difference in proportions (women minus men) falls within the given interval. This does not imply causality or the direction of preference in terms of "strictness" of legislation, but rather the proportion favoring stricter legislation.