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A simple random sample of 140 residents in a city was polled the week after the Game of Thrones finale, and 75 of them said they'd watched the finale. a) Construct a 95% confidence interval for the population of the residents of the city who watched Game of Thrones. b) Season 7 of Game of Thrones was the third most watched TV program in this city's history, with 48.1% of TV sets in America tuned in. Someone claims that the percentage of people who watched this season in this city was less than 48.1%. Does the confidence interval contradict this claim? Explain.c) Use the results from the sample of 140 to estimate the sample size necessary for a 95% confidence interval to have a margin of error of 0.025.

Question

A simple random sample of 140 residents in a city was polled the week after the Game of Thrones finale, and 75 of them said they'd watched the finale. 

a) Construct a 95% confidence interval for the population of the residents of the city who watched Game of Thrones. 

b) Season 7 of Game of Thrones was the third most watched TV program in this city's history, with 48.1% of TV sets in America tuned in. Someone claims that the percentage of people who watched this season in this city was less than 48.1%. Does the confidence interval contradict this claim? Explain.

c) Use the results from the sample of 140 to estimate the sample size necessary for a 95% confidence interval to have a margin of error of 0.025. 

check_circleAnswer
Step 1

In this question we have given the data, on the basis of data we have to calculate the Confidence interval, conduct the hypothesis testing and sample size 95% confidence interval to have a margin of error of 0.025

Step 2

Part A)

Here I have calculated the confidence interval, for the population of residents of the city who watched game of thrones.

Calculations have shown on whiteboard.

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Step 3

Part B)

Now on the basis of confidence interval calculated in last part we have test whether the claim made by a person that the percentage of people who watched this season in this city was less than 48.1%.

Calculations have shown on whiteboard.

  • Since the null hypothesis p = 0.481, lies in the con...
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Statistics

Hypothesis Testing

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