Previously, an organization reported that teenagers spend 12.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is lower. Twenty-three randomly chosen teenagers were asked how many hours per week they spend on the phone, with the following results (in hours): 10.4, 10.4, 17.3, 11.2, 10, 15.2, 9.5, 5.8, 12.5, 11.8, 7.3, 10.6, 11.5, 16.2, 16.5, 14.3, 12.3, 9.9, 13.7, 8.6, 11.3, 13, 16.5 Perform a hypothesis test using a 10% level of significance. Step 1: State the null and alternative hypotheses. Ho: p 12.5 H.: pv

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Previously, an organization reported that teenagers spend 12.5 hours per week, on average, on the
phone. The organization thinks that, currently, the mean is lower. Twenty-three randomly chosen
teenagers were asked how many hours per week they spend on the phone, with the following
results (in hours):
10.4, 10.4, 17.3, 11.2, 10, 15.2, 9.5, 5.8, 12.5, 11.8, 7.3, 10.6, 11.5, 16.2, 16.5, 14.3, 12.3, 9.9, 13.7, 8.6,
11.3, 13, 16.5
Perform a hypothesis test using a 10% level of significance.
Step 1: State the null and alternative hypotheses.
Ho: pv
12.5
12.5
(So we will be performing a left-tailed
Vv test.)
Step 2: Assuming the null hypothesis is true, determine the features of the distribution of
point estimates using the Central Limit Theorem.
By the Central Limit Theorem, we know that the point estimates are t-distributed
with
distribution mean
and distribution standard deviation
Step 3: Find the p-value of the point estimate.
= P(tv sv
p-value =
Step 4: Make a Conclusion About the nulI hypothesis.
= a, we do not reject
v the null
Since the p-value =
hypothesis.
rnand less than an average of 12,5 hours per week on the
Transcribed Image Text:Previously, an organization reported that teenagers spend 12.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is lower. Twenty-three randomly chosen teenagers were asked how many hours per week they spend on the phone, with the following results (in hours): 10.4, 10.4, 17.3, 11.2, 10, 15.2, 9.5, 5.8, 12.5, 11.8, 7.3, 10.6, 11.5, 16.2, 16.5, 14.3, 12.3, 9.9, 13.7, 8.6, 11.3, 13, 16.5 Perform a hypothesis test using a 10% level of significance. Step 1: State the null and alternative hypotheses. Ho: pv 12.5 12.5 (So we will be performing a left-tailed Vv test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are t-distributed with distribution mean and distribution standard deviation Step 3: Find the p-value of the point estimate. = P(tv sv p-value = Step 4: Make a Conclusion About the nulI hypothesis. = a, we do not reject v the null Since the p-value = hypothesis. rnand less than an average of 12,5 hours per week on the
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