2 a) The management of XYC Inc. wants to determine whether there is a significant

difference in the average length of time (in minutes) employees spent on Emails every day

within its two operating divisions. The following data has been accumulated for this test. The

degrees of freedom (df) for this problem are given to be df = 60.

Division 1 Division 2 Sample Mean 45.8 48.3 Sample Standard Deviation 10.2 18.6 Sample

Size 53 42

a) What is the set of null and alternative hypothesis if we want to determine whether the

average length of time employees spent on Emails within its two operating divisions is

the same? (2 Points)

b) Using a level of significance of 0.05, what is the rejection rule for this test using the

critical value approach? (2 Points)

Given Df=60

This is a two tailed test

Critical t with 0.05 level=2.0003

Rejection rule: Reject Ho if calculated t < -2.0003 or >;2.0003

c) Calculate the t statistic. (2 Points)

t=-0.377

d) Based on the above, what is the conclusion of this statistical test if the level of

significance is 0.05? (2 Points)

2 b) Salary information regarding male and female employees of a large company is

shown below.

Male Female Sample Size 64 36 Sample Mean Salary (in 1,000) 44 41 Sample Standard

Deviation 128 72

a) What is the set of null and alternative hypothesis if we want to determine whether the mean

salary of male and female employees is the same? (2 Points)

b) Using a level of significance of 0.05, what is the rejection rule for this test using the critical

value approach if the degrees of freedom (df) for this test is given to be df = 97? (2 Points)

c) Calculate the t statistic (2 Points)

d) Based on the above, what is the conclusion of this statistical test? (2 Points)

3 a) The average length of time customers spent on waiting at ABC Store's check-out

counter before a new P.O.S. system was installed was 5.1 minutes. A sample of 49 customers

randomly selected at the check-out counter after the new P.O.S. system was installed showed

that the average waiting time was 4.55 minutes with a sample standard deviation of 1.45 minutes.

We wish to determine if there has been a significant decrease (from 5.1 minutes) in the average

waiting time after the P.O.S. system was installed

a) State the null and alternative hypotheses to be tested. (2 Points)

b) Compute the test statistic. (2 Points)

c) Determine the critical value for this test at the 0.05 level of significance. (2 Points)

d) What do you conclude at the 0.05 level of significance? (2 Points)

e) Construct a 95% confidence interval for the average waiting time after the new P.O.S. system

was installed. (2 Points)

3 b) The average sales per store of ABC Inc.'s best-selling product in a supermarket

chain last year was $12,000. A random sample of 61 stores selected from the chain shows that

this year the average sales per store is $13,500 with a sample standard deviation of $12,000. We

wish to determine if there has been a significant increase in the average sales (from $12,000) per

store.

a) State the null and alternative hypotheses to be tested. (2 Points)

Null hypothesis: u < 12,000

Alternative hypothesis: u > 12,000

b) Compute the test statistic. (2 Points)

SE = s / sqrt(n)

S.E = 1536.443

DF = n - 1

D.F = 60

t = (x - u) / SE

t = 0.976

c) Determine the critical value for this test at the 0.05 level of significance. (2 Points)

d) What do you conclude at the 0.05 level of significance? (2 Points)

e) Construct a 95% confidence interval for the average sales per store this year. (2 Points)

C.I=

C.I=13500

C.I=13500

C.I=(10427.11,16572.89)

5 a) Below you are given the ages of a sample of 10 college students who are enrolled

in statistics.

2 19 20 22 24 24 29 31 34 85

a) Compute the median (2 Points)

Median = mean of (5th observation + 6th observation)

=(24+24)/2 = 24

b) Determine the 25th percentile. (2 Points)

25th percentile = first quartile

= Median of (2, 18, 20, 22, 24)

= 3rd observation

= 20

c) Determine the range (2 Points)

range = maximum observation - minimum observation

= 85 - 2 = 83

d) Determine the IQR (2 Points)

3rd quartile = median of ( 24, 29, 31, 34, 85)

= 3rd observation

= 31

IQR = 3rd quartile - 1st quartile

= 31 - 20 = 11

e) Identify all outliers, if any. (2 Points)

2, and 85

Question 5B A sample of 9 mothers was taken. The mothers were asked the age of their oldest

child. You are given their responses below.

3 22 25 25 29 31 33 38 41

a) Compute the median (2 Points)

3

Median =

= =29

b) Determine the 25th percentile. (2 Points)

= x 9= 2.25

=22

c) . Determine the range (2 Points)

R=41-3

= 38

d) Determine the IQR (2 Points)

Iqr= Q3-Q1=29

=7

e) Identify all outliers, if any. (2 Points)

OUTLINERS =3