The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let x = the number of sick days they took for the past year. Construct a 95% confidence interval for the true mean or proportion. Round to the nearest hundredth (2 decimal places).

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The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let x = the number of sick days they took for the past year.

Construct a 95% confidence interval for the true mean or proportion. Round to the nearest hundredth (2 decimal places).

 

Expert Solution
Working
x (x-xbar)^2
12 13.14063
4 19.14063
15 43.89063
3 28.89063
11 6.890625
8 0.140625
6 5.640625
8 0.140625

 

The mean is given by

\overline{x} = \frac{1}{n}\sum x

\overline{x} = \frac{67}{8} =8.375

 

The standard deviation is given by

s =\sqrt{\frac{1}{n-1}\sum (x - \overline{x})^2}

s =\sqrt{\frac{117.875}{7}} =4.1036

 

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