Question

Addicted to the Internet?The Ann Arbor public school officials would like to estimate the population mean daily Internet usage time for all Ann Arbor teens. To do so, a large random sample of Ann Arbor teens was selected. Here are the results of their study. The 95% confidence interval for the mean daily internet usage time for the population of all such Ann Arbor teens was found to be (6.7 hours, 9.3 hours).The 99% confidence interval or the mean daily internet usage time for the population of all such Ann Arbor teens was found to be (6.257 hours, 9.743 hours).The Ann Arbor public school officials know that you have some statistical background and would like your opinion. Please read each statement carefully and share with us your opinion.

Answer 1

To conduct a hypothesis test, set up the null and alternative hypotheses, calculate the z-score, find the p-value, and make a decision based on the p-value.

Step-by-step explanation:

To conduct a hypothesis test, we need to set up the null and alternative hypotheses. In this case, the null hypothesis is that the mean phone usage time is equal to 4.5 hours per week, and the alternative hypothesis is that the mean is higher than 4.5 hours per week.

Next, we calculate the test statistic, which is the z-score. The formula for the z-score is (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Using the given values, we can calculate the z-score.

Once we have the z-score, we can find the p-value associated with it. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Based on the p-value, we can make a decision. If the p-value is less than the significance level (a), we reject the null hypothesis. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis.

Answer 2

We can assure the Ann Arbor officials that after look the information we conclude that the mean is 8 h

Step-by-step explanation:

From CI ( 95 % ) = ( 6,7 ; 9,3 )

And the information "large random size sample" we conclude that the population has a normal distribution; a normal distribution has a bell shape curve, and data must spread symmetrically with respect to the mean, therefore the mean is:

6,7 + 9,3 = 16

16/2 = 8

If we need t check we can use the other CI

CI ( 99 % ) = (6,257 , 9,743 )

6,257 + 9,743 = 16

16/2 = 8

We are sure the mean is 8 h