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.

 

 

 

  Males   7,040 6,576 1,664 12,919 8,605 22,220 3,377 10,128 7,723 2,063 8,033 9,463 7,656 11,456 12,244 6,670 12,371 9,626 5,472 16,175 8,383 623 6,797 10,160 8,725 14,029 13,763 8,811 11,480 9,544 15,048 5,544 10,652 11,267 10,126 8,796 13,351 7,120 9,505 9,571 7,551 5,811 9,119 9,732 5,286 5,254 7,550 11,015 12,403 12,703   Â

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Source: USA TODAY.

 

 

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.

25 20 26 24 27 26 18 19 18 30 26 18 18 19 32 23 19 19 18 29 19 22 18 22 26 19 19 21 23 18 20 18 22 21 19 21 21 22 18 20 Females                                                      19 23             10,333          6,407         10,082          5,933           3,991                                           Commuter students                             7,435 8,324 6,989 16,249 5,922 18 20 19 18 22 25 24 35 7,654 8,411 11,324 10,248 6,030 23 18 23 22 28 25 20 24 9,331 6,869 6,502 11,041 11,597 26 30 22 22 22 21 18 20 5,468 7,874 9,277 10,127 13,371 19 26 35 19 19 18 19 32 7,055 6,909 8,903 6,925 7,058 29 23 21 19 36 27 27 20 12,745 12,016 9,883 14,698 9,907 20 21 18 19 23 20 19 19 8,917 9,110 5,232 6,959 5,832 20 25             7,054 7,235 11,248 8,478 6,502                 7,300 993 6,815 9,959 10,353 17.  Prob lem-Solving Ability  T wo groups of st udents are   Â

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.