Question

19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8

Use the above data and a 0.01 significance level to test the claim that the BMI has a standard deviation that is equal to 1.34, which is the standard deviation for the winners in the 20s and 30s.

A) Write down the claim.

B) Write down the null hypothesis and the alternative hypothesis. Indicate which one is the claim.

c) Draw the probability distribution curve. Write down the testing statistic and the P-Value on the graph.

d) Determine whether to reject the null hypothesis. Write the conclusion in a complete sentence.

Answer 1

Test and CI for One Variance: C1

Method

σ: standard deviation of C1

The Bonett method is valid for any continuous distribution.

The chi-square method is valid only for the normal distribution.

Descriptive Statistics

N	StDev	Variance	99% CI for σ using Bonett	99% CI for σ using Chi-Square
10	1.19	1.41	(0.75, 2.53)	(0.73, 2.70)

Test

Null hypothesis	H₀: σ = 1.34
Alternative hypothesis	H₁: σ ≠ 1.34

Method	Test Statistic	DF	P-Value
Bonett	—	—	0.606
Chi-Square	7.05	9	0.737

(A)-> Claim is BMH has standard deviation of 1.34.

(B)-> H₀: σ = 1.34   H₁: σ ≠ 1.34

(C)->

(D)->

Since the p-value is greater than level of significance, we don't have sufficient evidence to reject the null hypothesis at 1% level of significance. so Ho can't be rejected.

Hence the BMI has the standard deviation equal to 1.34.