Multiple Choice. For each of the following clearly place the one letter to the most correct answer in the blank provided. ( 5 points each )

 

 

_________      1. )       If I want to place a  90 %  confidence interval on the mean,  

is unknown, and the sample size is 23, what table value will I use?

 

                                                U. )  1.65         V. )  1.73         W. )  1.72      X. )  1.64  

Y. )  I need to know more information first.

 

 

 

_________      2.  )      In hypothesis testing, a Type I error occurs when ?

 

U.     )  Reject H, when His true                 

V.     )  Fail to Reject H, when H is true     

W.   )  Reject H, when H is false               

X.     )  Fail to Reject H,  when H is false

Y.  )   never occurs

 

 

 

_________      3.  )      If you are performing a hypothesis test and you Fail to Reject

the Null Hypothesis when H0 is true then you have :

 

U.  )   committed a Type I  error.     

V.  )   committed a Type II error.     

                                    W. )   not committed an error. 

                                    X.  )    need to know the hypothesis.

Y.  )    not enough information.

 

 

_________      4.  )      If the p-value of a hypothesis test is .058 and  then

 

                                    U.  )     Reject H

                                    V.  )     Fail to Reject H

                                    W. )     Accept H

X.  )     too close to tell.

Y.  )     not enough information.

 

 

_________      5. )       A sample of 36 job seekers took an average of 5.9 months to

find a new job. If the population standard deviation is 0.8 months, find the 95% confidence interval for the mean.

U.  )     (5.64, 6.16)     V.  )     (5.68, 6.12)
W. )     (5.86, 5.94)      X.  )     (5.56, 6.24)
Y.  )     (5.48, 6.32)

 

 

 

 

_________      6. )       A tourism group wishes to estimate the average cost of a

lobster dinner for their city within $0.50 with 95% confidence. It is known that the standard deviation of prices is $2.25. How large of a sample size should the group take?

U.  )     1         V.  )     9         W. )     78
X.  )     88       Y.  )     7780

 

 

 

_________      7. )       Find the appropriate critical value to use in a 99% confidence

interval for the mean when  is known and the sample size is 18?

U.  )     2.58     V. )      2.88     W. )     2.90
X.  )     1.96     Y. )      1.65

 

_________      8. )       A survey of 80 families showed that 36 of them had at least two

TV sets at home. Find the 90% confidence interval for the proportion of families with at least two TV sets.

U.  )     (29.76, 42.24)              V.  )     (0.364, 0.536)
W. )     (0.359, 0.541)              X.  )     (0.445, 0.455)
Y.  )     (0.407, 0.493)

 

 

________        9. )       A pharmaceutical company wishes to market a new product to

consumers over the age of 50. They plan to advertise on a certain TV show if the average age of the viewer is over 50. What hypotheses should the company test?

U.  )     H0:  vs. Ha:
V.  )     H0:  vs. Ha:
W. )     H0:  vs. Ha:
X.  )     H0:  vs. Ha:
Y.  )     H0: vs. Ha: > 50

 

________        10. )     Two new processing methods are tested at a factory. It is

hypothesized that there is no difference in the variances of the time needed to process products. A sample of 11 products using Process A show a variance of 4.5 minutes and a sample of 8 products using process B show a variance of 5.2 minutes. Using a 0.05 level of significance, we want to determine if there is a difference in the variances of the two processes. If we use the test statistic F = 5.2/4.5 = 1.56 , what is the appropriate rejection region?

U.  )     Reject Ho if F > 3.14
V.  )     Reject Ho if F > 3.14 or F < 0.275
W. )     Reject Ho if F > 4.76 or F < 0.253
X.  )     Reject Ho if F > 3.95 or F < 0.210
Y.  )     Reject Ho if F > 3.51 or F < 0.238

________        11. )     A study of corporate business costs was conducted to

determine if there was a difference between the average amount spent on dinner by executives and the average amount spent on dinner by managers. What is the value of the test statistic in this test of hypothesis?

 

Executives

Managers

Sample Mean

25.50

22.50

Sample Standard Deviation

4.75

2.83

Sample Size

32

35

U.  )     1.960   V.  )     3.172   W. )     6.338
X.  )     3.104   Y.  )     6.265

_________      12. )     In a wage discrimination case involving male and female

employees, independent samples of male and female employees with 5 years or more experience provided the following hourly wage results. We wish to conduct a test of hypothesis using a 0.05 level of significance in order to determine if the average hourly wage of the male workers is exceeds the average hourly wage of the female workers. What are the appropriate degrees of freedom for this test?

 

Male

Female

Sample Mean

$9.25

$8.70

Sample Standard Deviation

$1.00

$0.80

Sample Size

21

19

 

U.  )     20        V.  )     38        W. )     19
X.  )     21        Y.  )     18

__________    13. )     Independent random samples selected from two normal

populations produced the following results.

 

Sample 1

Sample 2

Sample Mean

5.4

4.9

Sample Standard Deviation

3.4

4.8

Sample Size

17

12

We wish to conduct a test of hypothesis to determine if the population means of these two samples are different. Using a 0.05 level of significance, what is the appropriate critical region for this test?

U.  )     Reject Ho if t > 1.96 or t < -1.96
V.  )     Reject Ho if t > 1.73 or t < -1.73
W. )     Reject Ho if t > 2.05 or t < -2.05
X.  )     Reject Ho if t > 2.09 or t < -2.09
Y.  )     Reject Ho if t > 2.12 or t < -2.12

 

For the remaining Hypothesis tests you must show all six steps of the test.

 

14. )     At a certain store, the amount of air pressure in new tires is supposed to be 35 lbs.  A random sample of  size 8 has a mean of  38 . 214 and a standard deviation of  2 . 9347 .  Test whether or not the average pressure in the tires is 35 lbs at the  0. 01 significance level.  (  9 points  )

 

 

15. )     We wish to prove that a new leavening process has decreased the average

number of calories per loaf of bread.  A random sample of 50 loaves taken with the new process has a sample mean of 1255 calories and a sample standard deviation of 215.  A random sample of 35 loaves taken with the old process has a sample mean of 1330 calories and a sample standard deviation of 238.  Perform a hypothesis test at the 0.10 significance level. ( 10 points )

16. )     Trace metals in drinking water affect the flavor, and unusually high

concentrations can pose a health hazard.  Six river locations were selected for a study and the zinc concentration (mg/L) was determined for both surface water and bottom water at each location.  Does the data in the table below at suggest that the true average concentration in bottom water exceeds that of surface water ? ( 16 points )

 

                                                                           Locations

Zinc Concentration                    1          2          3          4          5          6

 

Bottom water                          .430     .266     .567     .531     .707     .716

Surface water                         .415     .238     .390     .410     .605     .609