MATHEMATICS

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

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