The mean number of sick days an employee takes per year is believed to be about

Question

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 employees. The number of sick days they took for the past year are as follows: 11; 5:15; 4:10; 9; 6; 9, Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. Part (b) State the altemative hypothesis. Part (c) In words, state what your random variable X represents. represents the average number of employees that call out sick for 10 days in one year R represents the number of sick days an employee takes in one year represents the average number of sick days employees take each year. O R represents the average number of employees that call out sick on a given day. Part (d) State the distribution to use for the test. (Enter your answer in the form z or t,where d is the degrees of freedom.) Part (e) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

Explanation / Answer

Ans:

Sample size,n=8

sample mean=8.625

sample standard deviation=3.583

d)We will use t distribution with degree of freedom 7,as population standard deviation is unknown and n<30

e)3.583/sqrt(8)=1.267

Test statistic:

t=(8.625-10)/1.267=-1.085

f)p-value(2 tailed)=0.3139

(second option is correct)

g)Bottom right is correct.

h)alpha=0.05

As,p-value>0.05,we fail to reject H0.

i)95% CI

=8.625+/-2.365*(3.583/sqrt(8)

=8.625+/-3

=5.625,11.625

=(5.63,11.63)

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