Managerial Statistics: The Essentials

Question A

Question B

In this question we will use the z hypothesis test.

Since the alpha level is  , the z critical value is 

Therefore, because the z statistic is less than the critical value then we reject the null hypothesis and accept the alternate hypothesis and accept the population mean is greater than 

Question C

Assuming that the names of the groups are A, B, C and D. The hypotheses are as follows

Using Excel, I performed ANOVA analysis and found. The excel sheet is attached.

Conclusion

Since the p-value (0.208346) is not less than 0.05, we fail to reject the null hypothesis.

Question D

We know that 

From the question  therefore using normal approximation becomes 

We also know that  therefore we can determine the mean and the standard deviation.

The mean therefore is

We are asked to compute  . To find this probability we need to find the z score

Therefore,

Using the z table we establish that the probability of being less than z score of  is  and the probability of being less than z score of  is 0.6915.

To determine this  . We do

Therefore 

Question E

We are given 

Therefore, 

Using Z score table we find the probability that 

Question F

We are given 

Therefore, 

For the z score  , probability is  and for z score is  the probability is  . Therefore, the probability that  is  which is 6.68% and the probability that  is 30.85%.