Question

Gender	Armspan
Male	174.0
Female	163.0
Male	200.5
Female	174.0
Female	162.0
Female	162.5
Male	193.0
Female	172.5
Female	163.0
Female	195.5
Male	170.0
Male	181.0
Female	168.0
Female	168.0
Male	185.0
Female	170.0
Female	168.5
Female	162.0
Male	169.0
Female	164.5
Female	165.5
Male	177.5
Female	174.0
Female	175.0
Male	174.5
Male	173.0
Female	160.0
Female	172.0
Male	180.0
Female	173.0
Male	178.0
Male	185.5
Female	154.5
Female	170.0
Female	170.0
Female	171.0
Female	157.5
Male	185.0
Female	161.5
Female	155.0
Female	160.5
Female	180.5
Female	162.5
Male	168.0
Male	169.5
Female	150.0
Female	152.5
Female	163.0
Female	158.0
Female	167.5
Female	152.0
Female	159.5
Female	160.0
Female	152.5
Female	157.0
Female	167.5
Male	177.5
Female	174.0
Male	192.5
Female	160.0
Male	193.0
Male	175.0
Male	184.0
Female	154.0
Male	194.0
Male	182.5
Female	142.0
Female	160.0
Female	157.0
Female	163.0
Male	188.0
Male	180.0
Female	150.0

has been claimed that the mean armspan of adults in the US is greater than 166 cm. Does the data of our statistics class support or contradict this claim? Justify your answer through a formal hypothesis testing procedure with a P-value approach using a significance level of your choice. Calculation of and interpretation of the P-value is required on this problem.

H0:

H1:

Sample's Mean (x-bar):

Sample's S.D. (s):

Sample's Test Statistic:

P-value:

CONCLUSION:

Answer 1

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

sample mean = 169.664

Now we have to find sample standard deviation.

Excel command is =STDEV(Select data)

standard deviation = 12.314

T test

n = 73

s = 12.314

Null and alternative hypothesis is

H0 : u = 166

H1 : u > 166

Level of significance = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 73 - 1 = 72

P-value = 0.0066 ( using t table)

P-value , Reject H0

conclusion : There is sufficient evidance to conclude that the mean armspan of adults in the US is greater than 166 cm.