Question

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.; At a significance level of; a; = 0.05, what is the correct conclusion?

a. Reject the null hypothesis and conclude that the mean phone usage is higher.

b. Fail to reject the null hypothesis and conclude that the mean phone usage is not higher.

c. Reject the null hypothesis and conclude that the mean phone usage is not higher.

d. Fail to reject the null hypothesis and conclude that the mean phone usage is higher.

Answer 1

To conduct a hypothesis test, compare the test statistic to the critical value from the t-distribution to make a conclusion about the mean phone usage.

Step-by-step explanation:

To conduct a hypothesis test, we need to set up the null and alternative hypotheses and determine the test statistic and critical value. In this case, the null hypothesis (H0) is that the mean phone usage is still 4.5 hours per week, while the alternative hypothesis (Ha) is that the mean phone usage is higher than 4.5 hours per week.

Next, we calculate the test statistic, which is the t-score. The formula for the t-score is: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Plugging in the values from the question, we get: t = (4.75 - 4.5) / (2.0 / sqrt(15)) = 0.25 * sqrt(15) / 2.0.

Finally, we compare the calculated test statistic to the critical value from the t-distribution with (sample size - 1) degrees of freedom at the given significance level (0.05). If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean phone usage is higher. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean phone usage is higher.