Question

Suppose that we are to conduct the following hypothesis test:

H_0: mu = 980
H_1: mu > 980
Suppose that you also know that sigma = 250, n = 90, x = 1030, and take a = 0.05. Draw the sampling distribution, and use it to determine each of the following:
A. The value of the standardized test statistic:
B. The rejection region for the standardized test statistic:
C. The p-value is
D. Your decision for the hypothesis test. A. Do Not Reject H_1 B. Do Not Reject H_0. C. Reject H_0. D. Reject H_1.

Answer 1

To conduct the hypothesis test, we calculate the standardized test statistic, find the rejection region, determine the p-value, and make a decision based on the test statistic and p-value. In this case, we reject the null hypothesis.

Step-by-step explanation:

To determine the value of the standardized test statistic, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

Substituting the given values, we get:

z = (1030 - 980) / (250 / sqrt(90)) = 2.52

The rejection region for the standardized test statistic depends on the chosen significance level. For a = 0.05, the rejection region is z > 1.645.

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true. To find the p-value, we can use the z-table or calculator and find the area to the right of the test statistic. For z = 2.52, the area to the right is approximately 0.0059.

Based on the calculated test statistic and the rejection region, we compare the test statistic to the critical value and the p-value to the chosen significance level. In this case, the test statistic (2.52) is greater than the critical value (1.645) and the p-value (0.0059) is less than the significance level (0.05). Therefore, we reject the null hypothesis (H_0) in favor of the alternative hypothesis (H_1). So the correct answer is D. Reject H_1.