Question

A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: 12​13​14​14​15​15​15​16​16​16​16​16 17​17​17​18​18​18​18​19​19​19​20​21 The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours. A) What are the correct null and alternative hypotheses? B) What is the correct value of the test statistic? C) At α = 0.05, what conclusion we could make regarding null hypothesis? D) For a more accurate determination, top management wants to estimate the average number of hours volunteered per month by their professional staff to within one hour with 99% confidence. How many randomly selected professional employees would they need to sample? E) Suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. What is the 95% confidence interval?

Answer 1

A) Correct null and alternatives are as follows:

Null hypothesis: H0 : mu=15 (null hypothesis is always the hypothesis of "no difference".

Alternative hypothesis: H1 : mu>15 (they have to examine whether their claim of average working hours is greater than 15 or no)

For questions B) to D), i am attaching the R code and output. At the end i am also attaching image of all the formulas related to the test performed, in case you would want to know by hnad procedure.

B) the correct value of test statistic is, t=3.5817

C) We observe that the p value of the test is smaller than the level of significance (0.0007897<0.05).