Question

Show ALL work (or explain what was plugged into the calculator ) Use specific wording. Round to the thousandths place correctly when you are supposed to round.

A newspaper claims the mean weight of a US male is 180 pounds. But one think's it’s different. You collect the following SRS:

{190, 185, 188, 195, 170, 175, 190, 195, 190, 170, 124}

Is there sufficient evidence at the 5% significance level (α = .05) to indicate that the mean weight of US males is different than 180 pounds?

Ho:

H_a:

Test statistic:

p-val:

Statistical conclusion:

Conclusion in plain English:

Answer 1

Solution:

x	x2
190	36100
185	34225
188	35344
195	38025
170	28900
175	30625
190	36100
195	38025
190	36100
170	28900
124	15376
∑x=1972	∑x2=357720

Mean ˉx=∑xn

=190+185+188+195+170+175+190+195+190+170+124/11

=1972/11

=179.2727

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√357720-(1972)211/10

=√357720-353525.8182/10

=√4194.1818/10

=√419.4182

=20.4797

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 180

Ha :     180

Test statistic = t

= ( - ) / S / n

= (179.27-180 ) /20.48/ 11

= −0.118

Test statistic = t = −0.118

P-value =0.9082

= 0.05  

P-value >

0.9082 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to claim that the population mean μ is different than 180 , at the 0.05 significance level.