Question

Consider the following hypotheses: H0: μ = 70 HA: μ ≠ 70 Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) a. x¯ = 66; s = 12.0; n = 25 multiple choice 1 0.02 Picture p-value < 0.05 p-value Picture 0.10 0.01 Picture p-value < 0.02 p-value < 0.01 0.05 Picture p-value < 0.10 b. x¯ = 74; s = 12.0; n = 25 multiple choice 2 p-value Picture 0.10 0.05 Picture p-value < 0.10 0.02 Picture p-value < 0.05 0.01 Picture p-value < 0.02 p-value < 0.01 c. x¯ = 67; s = 11.3; n = 35 multiple choice 3 p-value Picture 0.10 p-value < 0.01 0.02 Picture p-value < 0.05 0.01 Picture p-value < 0.02 0.05 Picture p-value < 0.10 d. x¯ = 66; s = 11.3; n = 47 multiple choice 4 0.02 Picture p-value < 0.05 0.01 Picture p-value < 0.02 p-value Picture 0.10 p-value < 0.01 0.05 Picture p-value < 0.10

Answer 1

a. The p-value is less than 0.01.

b. The p-value is greater than 0.10.

c. The p-value is less than 0.01.

d. The p-value is greater than 0.10.

Step-by-step explanation:

In hypothesis testing, the p-value is a crucial measure used to determine the statistical significance of a test. The p-value represents the probability of obtaining results as extreme as the observed ones, assuming that the null hypothesis (H0) is true.

For part (a), with x¯ = 66, s = 12.0, and n = 25, the calculated p-value is less than 0.01. This indicates strong evidence against the null hypothesis, suggesting a rejection of H0 in favor of the alternative hypothesis (HA: μ ≠ 70).

In contrast, for part (b) with x¯ = 74, s = 12.0, and n = 25, the p-value is greater than 0.10. In this case, there is not enough evidence to reject the null hypothesis, and we fail to support the alternative hypothesis.

Similarly, for parts (c) and (d), the calculated p-values of less than 0.01 and greater than 0.10, respectively, lead to the same conclusions. The choice of the significance level (commonly set at 0.05) helps determine whether to reject the null hypothesis. In summary, a smaller p-value indicates stronger evidence against the null hypothesis, supporting the alternative hypothesis. Conversely, a larger p-value suggests a failure to reject the null hypothesis due to insufficient evidence.