Previously, an organization reported that teenagers spend 12.5 hours per week, on average, on thephone. The organization thinks that, currently, the mean is lower. Twenty-three randomly chosenteenagers were asked how many hours per week they spend on the phone, with the followingresults (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, 16.5Perform a hypothesis test using a 10% level of significance.Step 1: State the null and alternative hypotheses.Ho: pv12.5H.: pv12.5(So we will be performing a left-tailedVv test.)Step 2: Assuming the null hypothesis is true, determine the features of the distribution ofpoint estimates using the Central Limit Theorem.By the Central Limit Theorem, we know that the point estimates are t-distributedx and distribution standard deviation 3.024433vv withdistribution mean 3.024433Step 3: Find the p-value of the point estimate.P( Sv= P(tv svp-value =Step 4: Make a Conclusion About the null hypothesis.the null12.5X = a, we do not rejectSince the p-value =

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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 H.: P 12.5 (So we will be performing a left-tailed 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 x and distribution standard deviation 3.024433 vv with distribution mean 3.024433 Step 3: Find the p-value of the point estimate. P(tv p-value = Step 4: Make a Conclusion About the null hypothesis. the null ? v 12.5 X = a, we do not reject Since the p-value %3D

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 H.: P 12.5 (So we will be performing a left-tailed 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 x and distribution standard deviation 3.024433 vv with distribution mean 3.024433 Step 3: Find the p-value of the point estimate. P(tv p-value = Step 4: Make a Conclusion About the null hypothesis. the null ? v 12.5 X = a, we do not reject Since the p-value %3D

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

Topic Video

Question

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
H.: pv
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
x and distribution standard deviation 3.024433
vv with
distribution mean 3.024433
Step 3: Find the p-value of the point estimate.
P( Sv
= P(tv sv
p-value =
Step 4: Make a Conclusion About the null hypothesis.
the null
12.5
X = a, we do not reject
Since the p-value =

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