Question

A random sample of 100 observations from a population with standard deviation 14.88 yielded a sample mean of 92.6 . 1. Given that the null hypothesis is μ=90 and the alternative hypothesis is μ>90 using α=.05, find the following:

(a) Test statistic =
(b) P - value:
(c) The conclusion for this test is:
A. There is insufficient evidence to reject the null hypothesis
B. Reject the null hyporhesis
C. None of the above
2. Given chat the null hypothesis is μ=90 and the alternative hypothesis is μ
=90 using α=.05, find the following:
(a) Test statistic =
(b) P - value:
(c) The conclusion for this test is:

Answer 1

To test the hypothesis μ = 90 versus the alternative hypothesis μ > 90 with a sample of 100 observations, calculate the test statistic, p-value, and the conclusion for this test.

Step-by-step explanation:

To test the hypothesis μ = 90 versus the alternative hypothesis μ > 90 with a sample of 100 observations, we need to calculate the test statistic, p-value, and the conclusion for this test.

(a) Test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size)) = (92.6 - 90) / (14.88 / sqrt(100)) = 2.6 / 1.488 = 1.74

(b) P-value: The p-value is the probability of observing a test statistic as extreme as the one calculated under the null hypothesis. Using a t-distribution with 99 degrees of freedom, the p-value can be found to be approximately 0.043.

(c) The conclusion for this test is A. There is insufficient evidence to reject the null hypothesis.