Question

A claimed trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for recent Miss America winners. Use a 0.01 significance level to test the claim that recent winners are from a population with a mean BMI less than 18.5, which is considered underweight. Assume that the sample has been randomly selected from a population with a normal distribution. 19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8

Answer 1

Here the claim is that mean BMI is less than 18.5

As null hypothesis always have equality sign, so here hypothesis are

vs

For given sample mean value is

Create the following table.

data	data-mean	(data - mean)2
19.5	0.74	0.5476
20.3	1.54	2.3716
19.6	0.84	0.7056
20.2	1.44	2.0736
17.8	-0.96	0.9216
17.9	-0.86	0.73964
19.1	0.34	0.1156
18.8	0.04	0.0014
17.6	-1.16	1.3456
16.8	-1.96	3.8416

Find the sum of numbers in the last column to get.  

So standard deviation is

As distribution is normal but n<30, so we will use t test statistics

So P value is TDIST(0.07,9,1)=0.4729

As P value is greater than alpha=0.01, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean BMI is less than 18.5