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 greater than 4.5. ten randomly chosen teenagers were asked how many hours per week they spend on the phone. the level of significance is 0.05. the sample of teenagers’ time is: 3.0, 4.25, 5.5, 3.5, 7.0, 6.3, 2.0, 4.5, 3.7, 3.6, 7.2, 7.9

Answer 1

The question dealt with performing a hypothesis test to see if the mean time teenagers spend on the phone per week has increased from 4.5 hours. The process involves stating the null and alternative hypotheses, determining the level of significance, calculating the test statistic, and making a decision whether there is sufficient evidence to support the claim that the mean time has increased.

Step-by-step explanation:

The student's question involves conducting a hypothesis test to determine if the mean hours spent on the phone by teenagers have increased from the previously reported average of 4.5 hours. As given by the prompt, the organization believes the current mean to be higher and has collected a sample to test their assumption. To conduct this hypothesis test, key statistical elements such as the null hypothesis, alternative hypothesis, and the Type I error must be evaluated.

Steps for Hypothesis Testing:

1. State the null hypothesis (H0: μ = 4.5 hours) and the alternative hypothesis (Ha: μ > 4.5 hours).
2. Determine the level of significance, which is given as 0.05.
3. Calculate the test statistic using the sample mean (4.75 hours), sample standard deviation (2.0), and the sample size.
4. Compare the test statistic to the critical value from a z-table or t-table, given the level of significance and the degrees of freedom.
5. Make a decision about the null hypothesis based on whether the test statistic falls within the critical region.
6. Determine and report if there is sufficient evidence to support the claim that the mean time spent on the phone by teenagers is greater than 4.5 hours.

It is important to note that a Type I error in this context would be to incorrectly reject the null hypothesis when it is actually true.

At the 5 percent level of significance, if the test statistic falls within the critical region, we can conclude that there is sufficient evidence to reject the null hypothesis and support the organization's claim that the average time spent on the phone by teenagers is currently higher than 4.5 hours.