Hypothesis Test of 1 Mean 1· The mean number of sick days an employee takes per

Question

Hypothesis Test of 1 Mean 1· The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employ- ees. The number of sick days they took for the past year are as follows: 12;4; 15; 3; 11; 8; 6; 8 Should the personnel team believe that the mean number is about 10? Teststatistict=r-uand Confidence Interval ±E withE In rt State the null and alternative hypothesis State your conclusion for your hypothesis test. Give the 95% Confidence Interval. Give a conclusion for the confidence interval test. 4 points 4 points 4 points 4 points

Explanation / Answer

hypothesis:

null : Ho : u !=10

alternate : Ha : u =10

test static = 8.375 - 10/4.1036/sqrt(8)

= 1.12

critical value = +/-1.96

rejection region is -1.96 < X < 1.96

hence reject null hypothesis

so there not enough evidence to accept null hypothesis

margin of error = 1.96 * 4.1036/sqrt(8) = 2.8437

hence the confidence interval is [ 8.375 - 2.8437 , 8.375 + 2.8437] which is

[5.5313 , 11.2187]

we can say with 95% confidence that mean number of sick days will be between [5.5313 , 11.2187]

12 4 15 3 11 8 6 8 mean 8.375 standard deviation 4.103569874

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