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. Time2051206121622167216921712180218 32186219521962198220522102211

And the confidence interval would be given by (2137, 2203)

Step-by-step explanation:

2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210  ,2211

We can calculate the mean and deviation with these formulas:

(2)  

(3)  

And we got:

represent the sample mean for the sample  

population mean

s=48.72 represent the sample standard deviation

n=15 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

The degrees of freedom are given by:

Since the Confidence is 0.98 or 98%, the significance is and , and using excel we calculate the critical value

Now we have everything in order to replace into formula (1):

And the confidence interval would be given by (2137, 2203)

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