Question

As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article:

YF:	29,	35,	32,	27,	28,	32,	31,	35,	32,	27
OF:	18,	16,	23,	13,	12

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

Answer 1

H0: mean lean angles are the same for young and old

H1: mean lean angle for young is more than the old

We use independent sample t test assuming normality.

We calculate first summary statistics

N Mean StDev
yf 10 30.80 2.97
of 5 16.40 4.39

Since, Sd's are quite different,   we test for equality of population variances using F test and obtain a p value  0.304. Hence we conclude that population variances are not significantly different. Thus we use independent sample t test with equal variance. We calculate

Value of t statistic = 7.57 at DF=13 and a  P-Value < 0.0001 (.000 in 3 decimal point)

Hence we reject the null and conclude that  mean lean angle for young is significantly more than the old