Question

According to a marketing research study, American teenagers watched 16.5 hours of social media posts per month last year, on average. A random sample of 20 American teenagers was surveyed and the mean amount of time per month each teenager watched social media posts was 17.3. This data has a sample standard deviation of 2.1. (Assume that the scores are normally distributed). Researchers conduct a one-mean hypothesis at the 10% significance level to test if the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year. Which answer choice shows the correct null and alternative hypotheses for this test?

H0: μ = 17.3; Ha: μ< 17.3, which is a left-tailed test.
H0: μ = 17.3; Ha: μ > 17.3, which is a right-tailed test.
H0: μ = 16.5; Ha: μ < 16.5, which is a left-tailed test.
H0: μ = 16.5; Ha: μ > 16.5, which is a right-tailed test.

Answer 1

H0: μ = 16.5; Ha: μ > 16.5, which is a right-tailed test.

Explanation:

Given that:

the population mean μ = 16.5

the sample size n = 20

the sample mean
`\mathbf{\overline x}` = 17.3

the standard deviation σ = 2.1

level of significance = 0.10

The objective is to choose from the given options, the correct option that state the null hypothesis and the alternative hypothesis.

Given that; we want to determine if the mean amount of time they watch social media posts per month is greater than the mean amount of time last year, then we can say that the test is right-tailed.

Hence, the null hypothesis and alternative hypothesis can be computed as:

The null hypothesis:

`\mathbf{H_o: \mu = 16.5}`

The alternative hypothesis:

`\mathbf{H_1 : \mu > 16.5}`

Therefore, the fourth option is the right answer.