Questions: The government claims that the average age of Texans is 38 years. Blake hypothesizes that the average age of the population of Texas is not equal to 38 years. Blake records a sample mean equal to 41 and states the hypothesis as μ=38 vs μ ≠ 38. Select the best description for this type of test. a.) Upper-tailed test b.) Left-tailed test c.) Right-tailed test d.) Two-tailed test

The government claims that the average age of Texans is 38 years. Blake hypothesizes that the average age of the population of Texas is not equal to 38 years. Blake records a sample mean equal to 41 and states the hypothesis as μ=38 vs μ ≠ 38.

Select the best description for this type of test.
a.) Upper-tailed test
b.) Left-tailed test
c.) Right-tailed test
d.) Two-tailed test

Transcript text: The government claims that the average age of Texans is 38 years. Blake hypothesizes that the average age of the population of Texas is not equal to 38 years. Blake records a sample mean equal to 41 and states the hypothesis as $\mu=38$ vs $\mu \neq 38$. Select the best description for this type of test. a.) Upper-tailed test b.) Left-tailed test c.) Right-tailed test d.) Two-tailed test

Solution

Solution Steps

To determine the type of hypothesis test, we need to look at the null and alternative hypotheses. The null hypothesis ($H_0$) is that the population mean $\mu$ is equal to 38. The alternative hypothesis ($H_a$) is that the population mean $\mu$ is not equal to 38. Since the alternative hypothesis is testing for any difference (either greater than or less than), this is a two-tailed test.

Step 1: Identify the Hypotheses

The null hypothesis ($H_0$) is that the population mean $\mu$ is equal to 38, i.e., $H_0: \mu = 38$. The alternative hypothesis ($H_a$) is that the population mean $\mu$ is not equal to 38, i.e., $H_a: \mu \neq 38$.

Step 2: Determine the Type of Test

Since the alternative hypothesis is testing for any difference from 38 (either greater than or less than), this is a two-tailed test. A two-tailed test is used when we are interested in deviations in both directions from the hypothesized value.