Question

A large company is concerned about the commute times of its employees. Of the 333 employees who were surveyed, 131 said that they had a daily commute longer than 30 minutes. Create a 95% confidence interval for the proportion of employees who have a daily commute longer than 30 minutes. Use Excel to create the confidence interval, rounding to four decimal places

Answer 1

Answer:  (0.3409, 0.4459)

Step-by-step explanation:

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

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

Since , sample size : $n=333$

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

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

$\hat{p}=\dfrac{ 131}{333}\approx0.3934$

The confidence interval for population proportion is given by :-

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

$0.3934\pm(1.96)\sqrt{\dfrac{0.3934(1-0.3934)}{333}}\\\\\approx0.3934\pm0.0525\\\\=(0.3934-0.0525, 0.3934+0.0525=(0.3409,\ 0.4459)$

Hence,  a 95% confidence interval for the proportion of employees who have a daily commute longer than 30 minutes= (0.3409, 0.4459)

Answer 2

Answer:

0.3409, 0.4459

Step-by-step explanation: