P3 – where applicable, readings from tables must be used.

 

1.

The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours.  The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.

 

a)At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?

 

b)Compute the p-value and interpret its meaning.

 

c)Construct a 95% confidence interval estimate of the pupulation mean life of the light bulbs.

 

d)Compare the reuslts of (a) and (c).  What conclusions do you reach?

 

2.If, in a sample of n = 16 selected from a normal population, X ̅ = 56 and S = 12, what is the value of  tSTAT    if you are testing the null hypothesis H0: = 50?

 

3.In problem 2 above, how many degrees of freedom are there in the  t- test?

 

4.In problems 2 and 3 , what are the critical values of t if the level of significance,  α is 0.05 and the alternative hypothesis,  H1, is   ≠ 50?  

 

5.In problem 2, 3 and 4, what is your statistical decision if the alternative hypothesis,  H1 is  ≠ 50?  

 

6.In a training process, the average time taken is 6.4 hours.  Eight employees were trained using a new method and they had an average training time of 6.2 hours and a standard deviation of 1.1 hours.  Use α = 0.01 to determine if the new process reduced the training time.

 

Question 1

In testing for differences between the means of two related populations, the null hypothesis is

 

H0 :    D = 2.

 

H0 :   D = 0.

 

H0 :   D < 0.

 

H0 :   D > 0.

 

Question 2

A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.

 

Z = -2.55

 

Z = -0.85

 

Z = -1.05

 

Z = -1.20

 

 

Question 3

When testing H0 : π 1 – π 2  0 versus H1 :  π  1 – π  2 > 0, the observed value of the Z-score was found to be -2.13. The p-value for this test would be

 

 

0.0166.

 

0.0332.

 

0.9668.

 

0.9834.

 

 

 

Question 4

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.

s12  = 4      s22  = 6            

n1 = 16n2 = 25

 

df = 41

 

df = 39

 

df = 16

 

df = 25

Question 5

TABLE 10-1

 

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

AmericanJapanese

Sample size211100

Mean SSATL Score65.7579.83

Population Std. Dev.11.076.41

 

Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

H0 :   A –  J   0 versus H1 :   A –  J < 0

H0 :   A –  J   0 versus H1 :   A –  J > 0

H0 :   A –  J  = 0 versus H1 :   A –  J ≠ 0

H0 : X ̅ A – X ̅  J  0 versus H1 :   X ̅  A – X ̅  J ≠ 0

 

 

 

 

 

 

Question 6

TABLE 10-5

 

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

 

StudentExam score 

Before Course (1)Exam Score 

After course (2)

1530670

2690770

39101000

4700710

5450550

6820870

7820770

8630610

 

 

Referring to Table 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

 

2.365

 

2.145

 

1.761

 

1.895

Question 7

The t test for the difference between the means of 2 independent populations assumes that the respective

 

sample sizes are equal.

 

sample variances are equal.

 

populations are approximately normal.

 

All of these.

 

 

 

Question 8

TABLE 10-4

 

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

 

Gotham: X ̅G = 35 months, SG2  = 900  Metropolis: X ̅M = 50 months, SM2  =1050

 

 

Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?

 

-8.75

 

-3.69

 

-2.33

 

-1.96

Question 9

TABLE 10-4

 

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

 

Gotham: X ̅G = 35 months, SG2  = 900  Metropolis: X ̅M = 50 months, SM2  =1050

 

Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?

 

4.06

 

5.61

 

8.01

 

16.00

Question 10

Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test.

s12  = 4      s22  = 6            

n1 = 16n2 = 25 

 

sp2 = 6.00

 

sp2 = 5.00

 

sp2 = 5.23

 

sp2 = 4.00

Question 11

If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to

 

39.

 

38.

 

19.

 

18.

Question 12

In testing for differences between the means of two independent populations, the null hypothesis is:

 

H0 :  1 –  2 = 2.

 

H0 : 1 –  2 = 0.

 

H0 :  1 - 2 > 0.

 

H0 :  1 –  2 < 2.

 

 

 

 

 

Question 13

TABLE 10-5

 

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

 

 

StudentExam score 

Before Course (1)Exam Score 

After course (2)

1530670

2690770

39101000

4700710

5450550

6820870

7820770

8630610

 

 

Referring to Table 10-5, the value of the sample mean difference is ________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

 

0

 

50

 

68

 

400

 

 

 

 

 

 

 

 

 

 

Question 14

TABLE 10-1

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

AmericanJapanese

Sample size211100

Mean SSATL Score65.7579.83

Population Std. Dev.11.076.41

 

Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

 

paired t test

 

pooled-variance t test for the difference between two means

 

F test for the ratio of two variances

 

Z test for the difference between two proportions

Question 15

TABLE 10-3

 

The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Preservative IPreservative II

X ̅I = 106.4 hours  X ̅II = 96.54 hours  

SI  = 10.3 hours  SII  = 13.4 hours

 

 

 

 

 

 

 

Referring to Table 10-3, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.

 

H0 :  –  I2 –  II2     0 versus H1 :  I2 –  II2   < 0

 

H0 :  –  I2 –  II2      0 versus H1 :  I2 –  II2  > 0

 

H0 :  –  I2 –  II2   = 0 versus H1 :  I2 –  II2  ≠ 0

H0 :  –  I2 –  II2    ≠ 0 versus H1 :  I2 –  II2   = 0

 

 

 

 

 

 

 

 

 

 

 

Question 16

If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to

 

39.

 

38.

 

19.

 

18.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 17

TABLE 10-2

 

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Hypothesized Difference0

Level of significance0.05

Population 1 Sample

Sample size18

Sample Mean48266.7

Sample Standard Deviation13577.63

Population 2 Sample

Sample Size12

Sample Mean55000

Sample Standard Deviation11741.29

Difference in Sample Means-6733.3

t- Test Statistic-1.40193

Lower-Tail Test

Lower Critical value-1.70113

p-value0.085962

 

 

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is:

 

0.0860

 

-1.4019

 

-1.7011

 

-6,733.33

 

 

 

 

 

 

 

Question 18

TABLE 10-2

 

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Hypothesized Difference0

Level of significance0.05

Population 1 Sample

Sample size18

Sample Mean48266.7

Sample Standard Deviation13577.63

Population 2 Sample

Sample Size12

Sample Mean55000

Sample Standard Deviation11741.29

Difference in Sample Means-6733.3

t- Test Statistic-1.40193

Lower-Tail Test

Lower Critical value-1.70113

p-value0.085962

 

  

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?

 

H1 :  females >  males

 

H1 :  females <  males

 

H1 :  females ≠   males

 

H1 :  females =  males

 

 

 

 

 

 

Question 19

TABLE 10-1

 

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

AmericanJapanese

Sample size211100

Mean SSATL Score65.7579.83

Population Std. Dev.11.076.41

 

 

 

Referring to Table 10-1, what is the value of the test statistic?

 

-14.08

 

-11.8092

 

-1.9677

 

96.4471

Question 20

In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are

 

n – 1.

 

n1 + n2 – 1.

 

n1 + n2 – 2.

 

n – 2.