Question

In a random sample of 625 people, it was found that 225 of them frequently check their work email when they are at home. Find the upper confidence limit of a 95% confidence interval for p, the true proportion of people who frequently check their work email when they are at home. Give your answer to four decimal places

Answer 1

Answer: (0.3224,0.3976)

Step-by-step explanation:

Given : Sample size : n=625

Number of people check their work email when they are at home =225

The probability of people check their work email when they are at home :$p=\dfrac{225}{625}=0.36$

Significance level : $\alpha:1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

The confidence interval for population proportion is given by :-

$p \pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.36\pm(1.96)\sqrt{\dfrac{0.36(1-0.36)}{625}}\\\\=0.36\pm0.037632\\\\=(0.322368,0.397632)\approx(0.3224,0.3976)$