238 LINEAR REGRESSION AND CORRELATION Ch. 7 



the courtesy of Mrs. Ada Seymour and the Department of Home Economics, 

 Kansas Agricultural Experiment Station. All ages are to the nearest birthday. 



48. Fill in the two CI 95 's omitted above and state what information they 

 yield. 



49. Graph the CI 95 's versus age (on the horizontal axis) so as to produce a 

 figure from which you could read, approximately, the confidence interval on 

 true mean basal metabolism for any age, with a confidence coefficient .95. This 

 is to be applied only to Kansans, of course. 



50. Compute the two missing standard deviations in the above table. 



51. Test the hypothesis that Kansas women between the ages of 35 and 39 

 have a higher average basal metabolism than those in the age interval from 

 30 to 34 years. 



52. According to the "Mayo Foundation Normal Standards," published in 

 July of 1936 in the American Journal oj Physiology, the mean basal for 17-year- 

 old females is 37.82 calories per square meter per hour. According to the table 

 above do the Kansas girls fit that norm, or do they probably have a lower 

 average metabolism rate? How confident can you be of your answer when 

 allowance is made for sampling error in the above table, but none is allowed 

 for the Mayo Standard? 



53. Assuming that the records for those persons in the age group 21 to 25 

 years are normally distributed, estimate the range for this sample of 175. 



54. Suppose that 147 freshmen, 18 years of age, have taken a test designed 

 to measure their ability to think critically, and have taken this test at the 

 beginning and also at the end of their freshmen year. Their progress during 

 the year is measured by the difference between these two scores. Given that 

 2F = 712 and 2j/ 2 = 5567.40, test the hypothesis that freshmen of the sort so 

 sampled make some improvement in critical thinking during the year in so 

 far as this is measured by the test administered. Consider that t has 30 D/F. 



Ans. t = 9.67, P nearly zero; n ^ 0. 



