Question

data for the hypothesis test: • H₀ μ = 9.7. H₀ μ≠ 9.7 • Assume the significance level is a = 0.10. • The z- test statistic is calculated as 3.03. What is the p-value and conclusion for this hypothesis test?

Answer 1

To determine the p-value, look up the z-test statistic value in a standard normal distribution table. With a z-score of 3.03 in a two-tailed test, the p-value is approximately 0.0024, which is less than the alpha of 0.10. This leads to a rejection of the null hypothesis.

Step-by-step explanation:

The question asks us to determine the p-value and the conclusion of a hypothesis test with a given z-test statistic and significance level (alpha). Given that the z-test statistic is 3.03, we look up this value in a standard normal distribution table (or use technology) to find the corresponding p-value for a two-tailed test. Since the alternative hypothesis is non-directional (μ ≠ 9.7), we consider both tails of the distribution.

For a z-score of 3.03, the p-value in each tail of the normal distribution is approximately 0.0012. Because we have a two-tailed test, we double this value, giving us a p-value of 0.0024. With a significance level of 0.10, the p-value (0.0024) is less than alpha (0.10). Therefore, we reject the null hypothesis because there's sufficient evidence to suggest that the true population mean is different from 9.7.