Question

# Gender Armspan Male 174.0 Female 163.0 Male 200.5 Female 174.0 Female 162.0 Female 162.5 Male 193.0...

 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:

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.