Question

It is known that the mean of height of the population of women is 65 inches. A random sample of 18 supermodels was selected, and they had a mean height of 69.9 inches and a standard deviation of 1.2 inches. Use a 0.05 significance level to test the claim that mean heights of female supermodels are larger than the mean heights of women in general.

a.) Write the claim using an appropriate math expression

b.) Define the Null and Alternate Hypotheses

c.) Find the p-value

d.) Make your conclusion

Answer 1

so/ Given that mean of height of the poph- of women iş 65 inches and a sample is randomly Selected units from population of size 18 of super model have sample mean 69. ginches and Standard deviation 1.2 inches then (al if we suppose the mean of supermodels you thew Our claim le u>65, (b) our null hypothesiß is coli Hoid=65 ve alternative Wo: 4365 10 Tb (1-1) (6) To find p-value we have to calculate test statistics for this test- Here population standard deviation has not know and sample standard deviation to known so test statists for testing the mean to w to = ž-lo s/sn. M12 robin Here ã = 69. Mo 365, S31.2, n=18. so, to co 69.9,-6Sig Sibas!! Bracica 7.2/518 15 18.11.5: 2,0- Sinar = 4.9 x 1783 J:2= >1.03.19

to = 20.7889 1.2 to. = 17.3241 since the value of test statistic la positive and it to one sided test then P-value would be P-value = pltato P-value = P1+ >17.3241 = 0.0000 to il p-value is < 0.00001 ie The result la significant at p<0,05 (d) so the nell hypothesis may be rejected On the basis of sample value so accord roling to our test mean of super model will be greater than 65 inches le mean of height of the population of women.