Question

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A recent survey collected information on television viewing habits from a random sample of 1,000 people in the United States. Of those sampled, 37 percent indicated that their favorite sport to watch on television was American football.(a) Construct and interpret a 95 percent confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football.(b) Based on your answer to part (a), is it reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football? Justify your answer.

Answer 1

Explanation:

so basically multiply it by X

Answer 2

a)
`34\% \:<\:p\:<\:40\%`

b) No, it is not reasonable

Explanation:

According to the survey, 37 percent indicated that their favorite sport to watch on television was American football.

This means that:
`\hat p=(37)/(100)=0.37`

and
`\hat q=1-0.37=0.36`

Since
`\alpha=1-0.95=0.05`, we have:
`z_{(\alpha)/(2) }=1.96`

Substitute in the formula:

`\hat p- z_{(\alpha)/(2) }\sqrt{(\hat p \hat q)/(n) } \:<\:p\:<\:\hat p+ z_{(\alpha)/(2) }\sqrt{(\hat p \hat q)/(n) }`

This gives us:

`0.37- 1.96* \sqrt{((0.37)(0.63))/(1000) } \:<\:p\:<\:0.37+ 1.96* \sqrt{((0.37)(0.63))/(1000) }`

We evaluate to get:

`0.37- 1.96* 0.0153 \:<\:p\:<\:0.37+ 1.96* 0.0153`

We simplify to get:

`0.37- 0.029988 \:<\:p\:<\:0.37+ 0.029988`

This gives:

`0.340012 \:<\:p\:<\:0.399988`

Or

`34\% \:<\:p\:<\:40\%`

Part b)

From a) we obtain the confidence interval as
`34\% \:<\:p\:<\:40\%`.

This means we are 95% confident that, the actual percent of people in the United States whose favorite sport to watch on television is American football is between 34% and 40%.

Since 33% is less than 34%, it is not reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football