Question

A rectangular room has a population mean of 50. The alternative hypothesis states that the population mean is not equal to 50. The sample mean is 48 and the sample standard deviation is 11. Refer to exhibit 9-3. If the test is done at a 5

1) Cannot be determined
2) 1.82
3) 2.33
4) 1.96

Answer 1

The critical value for a two-tailed hypothesis test at a 5% significance level is usually 1.96, but the actual value may vary depending on the distribution, sample size, and the specifics of the test.

Step-by-step explanation:

The question pertains to statistics and specifically to hypothesis testing. In this scenario, a student is testing the hypothesis that the population mean of a rectangular room is not equal to 50. This is done using a sample mean of 48 and a sample standard deviation of 11. The question seems to be asking for the critical value at a 5% significance level but does not state whether it's a one-tailed or two-tailed test. Assuming it's a two-tailed test, the closest critical value for a 95% confidence interval (5% significance level) from a Z-table is typically 1.96. For other hypothesis testing scenarios, such as comparing two population means, determining if the population standard deviation is greater than a certain value, or testing a population proportion, different critical values and distributions might be used, such as t-distributions or Chi-square distributions, depending on the sample size and other parameters.