Question

Is there sufficient evidence at the α=0.10 level of significance to conclude that the population proportion of employees from the local company who borrowed against his or her 401(k) retirement plan in the last year is:

A) p≥0.17
B) p<0.17
C) p≠0.17
D) p≤0.17

Answer 1

Hypothesis testing uses a p-value to compare against a specified alpha level (0.10 in the question) to determine if there's sufficient evidence to reject the null hypothesis and support an alternative hypothesis about a population proportion.

Step-by-step explanation:

To determine if there is sufficient evidence at the alpha level of 0.10 to conclude that the population proportion of employees who borrowed against his or her 401(k) retirement plan is different from a certain value, a hypothesis test can be performed using the p-value obtained from the test statistic.

In this case, the null hypothesis (H0) would typically state that the proportion (p) is equal to the specified value (e.g., p = 0.17), while the alternative hypothesis (Ha) may be structured in one of the following ways, depending on the question:

• A) p ≥ 0.17 (Test for non-inferiority)
• B) p < 0.17 (Test for less than)
• C) p ≠ 0.17 (Two-sided test)
• D) p ≤ 0.17 (Test for non-superiority)

To reach a conclusion, one would compare the p-value from the test with the alpha level. If the p-value is less than the alpha level, the null hypothesis is rejected, suggesting that there is sufficient evidence to support the alternative hypothesis. Conversely, if the p-value is greater than the alpha level, the null hypothesis is not rejected. The provided examples demonstrate this decision-making process in various statistical scenarios.