Question

Both arm span and height are normally distributed among adult males and females. Most people have an arm span approximately equal to their height. This activity will use the data below taken from a spring 2014 Statistics class. Test the claim that the mean arm span is the same as the mean height. Use α= 0.05 as your level of significance.

Person #	Arm Span (cm)	Height (cm)
1	156	162
2	157	160
3	159	162
4	160	155
5	161	160
6	161	162
7	162	170
8	165	166
9	170	170
10	170	167
11	173	185
12	173	176
13	177	173
14	177	176
15	178	178
16	184	180
17	188	188
18	188	187
19	188	182
20	188	181
21	188	192
22	194	193
23	196	184
24	200	186

Test the hypothesis indicated above following the 8-step procedure we have discussed.

Answer 1

n1 = 24

n =24

s1 =13.590

s2 =11.237

claim : The mean arm span is the same as the mean height

Null and alternative hypothesis is

Vs

Level of significance = 0.05

Before doing this test we have to check population variances are equal or not.

Null and alternative hypothesis is

Vs

Test statistic is

F = Larger variance / Smaller variance = 184.6881 / 126.2702 = 1.4626

Degrees of freedoms

Degrees of freedom for numerator = n1 - 1 = 24 - 1 = 23

Degrees of freedom for denominator = n2 - 1 = 24 - 1 = 23

Critical value = 2.014                ( using f-table )

F test statistic < critical value , we fail to reject null hypothesis.

Conclusion: Population variances are equal.

So we have to use pooled variance.

Test statistic

Formula

,

d.f = n1 + n2 – 2 = 24 + 24 -2 = 46

p-value = 0.836  ( using t table )

p-value ,Failed to Reject H0

conclusion : There is a sufficient evidence that to conclude that the mean arm span is the same as the mean height