Question

A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 39 customers an average of 80 days to find a job. Assume the population standard deviation is 10 days. Construct a 95% confidence interval of the population mean number of days it takes to find a job.

a [60.8400, 99.1600]

b [76.3485, 83.6515]

c [76.8610, 83.1390]

d [77.4366, 82.5634]

Answer 1

Given that, sample size (n) = 39, sample mean = 80 days and

population standard deviation = 10 days

A 95% confidence level has significance level of 0.05 and critical value is,

The 95% confidence interval for the population mean is,

Therefore, required confidence interval is, (76.8615, 83.1385)

Answer : c) [ 76.8610, 83.1390 ]

Note : if we rounded to three decimal places then we will get required answer.