12. ACT Scores A survey of 1000 students nationwide showed a mean ACT score of 21.4. A survey of 500 Ohio scores showed a mean of 20.8. If the population standard deviation in each case is 3, can we conclude that Ohio is below the national average? Use a = 0.05.

Source: Report of WFIN radio.

 

 13.  Money Spent on College Sports  A school administrator hypothesizes that colleges spend more

for male sports than they do for female sports. A sample of two different colleges is selected, and the annual expenses (in dollars) per student at each school are shown. At a = 0.01, is there enough evidence to support the claim? Assume s1 = 3830 and s2 = 2745.

 

 

 

evidence to reject the claim of no difference in the ages of the two groups. Use the standard deviations from the samples and the P-value method. Assume s1 = 3.68 and s2  = 4.7.

 

                                Resident students                               

22        25        27        23         26        28        26        24

 

 14.  Monthly Social Security Benefits The average monthly Social Security benefit in 2004 for retired workers was $954.90 and for disabled workers wasgiven a problem-solving test, and the results are com- pared. Find the 90% confidence interval of the true difference in means.

Mathematics majors           Computer science majors

 

 

$894.10. Researchers used data from the Social Security

X1 = 83.6

X2 = 79.2

 

records to test the claim that the difference in monthly benefits between the two groups was greater than $30. Based on the following information, can the researchers’ claim be supported at the 0.05 level of significance?

Retired      Disabled

Sample size                                        60                60

Mean benefit                                 $960.50       $902.89 Population standard deviation                 $98         $101

Source: New York Times Almanac.

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