Question

Alice wants to estimate the percentage of people who plan on voting yes for the upcoming school levy. She surveys 380 individuals and finds that 260 plan on voting yes. Identify the values needed to calculate a confidence interval at the 90% confidence level. Then find the confidence interval.

Answer 1

Answer: (0.641, 0.719)

Step-by-step explanation:

The confidence interval for population proportion is given by :-

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

Given : Level of significance : $1-\alpha:0.90$

Then , significance level : $\alpha: 1-0.90=0.10$

Since , sample size : $n=380$ , i.e. a large sample.

Critical value : $z_{\alpha/2}=1.645$

Also, the proportion of individuals plan on voting yes :-

$\hat{p}=\dfrac{260}{380}\approx0.68$

Then , the confidence interval at the 90% confidence level will be :-

$0.68\pm(1.645)\sqrt{\dfrac{0.68(1-0.68)}{380}}\\\\\approx0.68\pm0.039\\\\=(0.68-0.039, 0.68+0.039=(0.641,\ 0.719)$

Hence, the confidence interval at the 90% confidence level= (0.641, 0.719)