Question

You want to test the hypothesis that the mean is less than 158 within a 5% level of significance. Your sample of 70 had a mean of 150.1 and a standard deviation of 61.62. Conduct a hypothesis test to determine if the mean is less than 158. Specify the null and alternative hypotheses and the significance level.

Answer 1

Null hypothesis (H0): The mean is greater than or equal to 158.

Alternative hypothesis (H1): The mean is less than 158.

Significance level: α = 0.05.

Step-by-step explanation:

In this scenario, the null hypothesis (H0) states that the population mean is greater than or equal to 158, while the alternative hypothesis (H1) suggests that the mean is less than 158. The significance level, denoted by α, is set at 0.05, indicating a 5% chance of rejecting the null hypothesis when it's true. To conduct the hypothesis test, the sample mean of 150.1 and the standard deviation of 61.62 are used.

Utilizing a one-sample z-test or t-test (depending on whether the population standard deviation is known), with the given sample mean, standard deviation, and sample size of 70, we would calculate the test statistic and compare it against the critical value or p-value associated with a significance level of 0.05. If the calculated test statistic falls in the critical region (in