Does the amount of TV people watch have anything to do with their religion? The General Social Survey determined that the average amount of TV Americans watch is 2.96 hours per day. 14 participants of the study described themselves as very religious. They reported their daily TV intake (in hours) as 1 1 1 2 2 2 2 3 3 4 4 4 4 5 Is this enough evidence to conclude that people who identify as very religious watch more (or less) TV than the average American public? (a) Verify that for this sample that the sample mean is 2.71 and the sample standard deviation is 1.33. (b) Compute a 95% confidence interval for the average amount of time that very religious Americans watch TV per day. Compare the confidence interval to the general American public. Do you think there is reason to say that very religious Americans watch more or less TV than the rest of America? (c) Conduct a 5-step hypothesis test to answer the question: Does the amount of TV very religious people watch on average differ from the general public? Obtain a p-value for your test and interpret its value (at significance level α= 0.05). Make sure to formulate your conclusion in the form of a complete sentence. (d) Do you see a relationship between the confidence interval you computed in (a) and the hypothesis test you conducted in (b)? Will the two methods always come to the same conclusion? Explain.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.6: Summarizing Categorical Data

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Does the amount of TV people watch have anything to do with their religion? The General Social Survey determined that the average amount of TV Americans watch is 2.96 hours per day. 14

participants of the study described themselves as very religious. They reported their daily TV intake (in hours) as

1 1 1 2 2 2 2 3 3 4 4 4 4 5

Is this enough evidence to conclude that people who identify as very religious watch more (or less) TV than the average American public?

(a) Verify that for this sample that the sample mean is 2.71 and the sample standard deviation is 1.33.

(b) Compute a 95% confidence interval for the average amount of time that very religious Americans watch TV per day. Compare the confidence interval to the general American public.

Do you think there is reason to say that very religious Americans watch more or less TV than the rest of America?

(c) Conduct a 5-step hypothesis test to answer the question: Does the amount of TV very religious people watch on average differ

from the general public? Obtain a p-value for your test and interpret its value (at significance level α= 0.05). Make sure to formulate your conclusion in the form of a complete sentence.

(d) Do you see a relationship between the confidence interval you computed in (a) and the hypothesis test you conducted in (b)? Will the two methods always come to the same conclusion? Explain.

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