Question

In a survey of 329 people who attended a local professional soccer team’s most recent home game, 141 said that they were fans of the visiting team. Create a 95% confidence interval for the population proportion of attendees who were fans of the visiting team. Use Excel to create the confidence interval, rounding to four decimal places.

Answer 1

Answer: (0.3751,0.4821)

Explanation:

Given : Level of significance :
`1-\alpha:0.95`

Then , significance level :
`\alpha: 1-0.95=0.05`

Since , sample size :
`n=329` , i.e. a large sample (n<30).

Then we use z-test.

Using excel (by going in formulas for more statistics and then statistics), Critical value :
`z_(\alpha/2)=1.96`

Also, the proportion of people said that they were fans of the visiting team :-

`\hat{p}=( 141)/(329)\approx 0.4286`

The confidence interval for population proportion is given by :-

`\hat{p}\pm z_(\alpha/2)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`0.4286\pm(1.96)\sqrt{(0.4286(1-0.4286))/(329)}\\\\\approx0.4286\pm0.053\\\\=(0.4286-0.0534, 0.4286+0.053=(0.3751,\ 0.4821)`

Hence, a 95% confidence interval for the population proportion of attendees who were fans of the visiting team= (0.3751,0.4821)