The mean number of sick days an employee takes per year isbelieved to be about 10. Members of a personnel department do notbelieve this figure. They randomly survey 8 employees. The numberof sick days they took for the past year are as follows: 12; 6; 15;5; 11; 10; 6; 8. Let X = the number of sick days they took for thepast year. Should the personnel team believe that the mean numberis about 10? Conduct a hypothesis test at the 5% level. Note: Ifyou are using a Student's t-distribution for the problem, you mayassume that the underlying population is normally distributed. (Ingeneral, you must first prove that assumption, though.) A.) Statethe distribution to use for the test. (Enter your answer in theform z or tdf where df is the degrees of freedom.) B.) What is thetest statistic? (If using the z distribution round your answers totwo decimal places, and if using the t distribution round youranswers to three decimal places.) C.) What is the p-value? (Roundyour answer to four decimal places.) D.) Indicate the correctdecision (\"reject\" or \"do not reject\" the null hypothesis), thereason for it, and write an appropriate conclusion. (i) Alpha(Enter an exact number as an integer, fraction, or decimal.) E.)Construct a 95% confidence interval for the true mean. Sketch thegraph of the situation. Label the point estimate and the lower andupper bounds of the confidence interval. (Round your answers tothree decimal places.)