Question

Calculate a Confidence Interval for the Mean, population standard deviation known - Calculator

Question

The number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. A sample of 15 people is selected at random, and the number of hours worked per year per person is given below. Calculate the 98% confidence interval for the mean hours worked per year in this state. Round your answers to the nearest integer and use ascending order.

Time

2051

2061

2162

2167

2169

2171

2180

2183

2186

2195

2196

2198

2205

2210

2211

Answer 1

Solution:

The 98% confidence interval for population mean is given as follows:

Where,  

is population standard deviation, n is sample size and Z(0.02/2) is critical z-value to construct 98% confidence interval.

We have, n = 15

Using Z-table we get, Z(0.02/2) = 2.3263

Hence, 98% confidence interval for the mean hours worked per year in the state is,

On rounding to nearest integer we get confidence interval as follows :

The 98% confidence interval for the mean hours worked per year in the state is (2146, 2193).

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