Question

Assume that a simple random sample is selected from a normally distributed population.

A study was conducted of babies born to mothers who use cocaine during pregnancy, and the following sample data were obtained for weights at birth: n = 192,  = 2700 grams, s = 651 grams.

a) Use a 0.05 significance level to test the claim that the standard deviation of birth weights of infants born to mothers who use cocaine is different from the standard deviation of 696 grams for birth weights of infants born to mothers who do not use cocaine during pregnancy.

Claim:   ---Select--- < > = ≠ ≤ ≥ 696

H_o:     ---Select--- < > = ≠ ≤ ≥ 696

H₁:     ---Select--- < > = ≠ ≤ ≥ 696

b) What is the rejection result?

Do not reject the null hypothesis.Reject the null hypothesis.    Not enough information.

c) What is the conclusion? Does cocaine use by mothers appear to affect the variation of the weights of their babies?

There is not significant evidence that  differs from 696 g. Cocaine use appears to affect the variation of weights.There is significant evidence that  differs from 696 g. Cocaine use does not appear to affect the variation of weights.    There is not significant evidence that  differs from 696 g. Cocaine use does not appear to affect the variation of weights.There is significant evidence that  differs from 696 g. Cocaine use appears to affect the variation of weights.

Answer 1

a)

claim:
H1: σ ≠ 696

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 696
Alternative Hypothesis, H1: σ ≠ 696

Rejection Region
This is two tailed test, for α = 0.05 and df = 191
Critical value of Χ^2 are 154.621 and 231.165
Hence reject H0 if Χ^2 < 154.621 or Χ^2 > 231.165

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (192 - 1)*651^2/696^2
Χ^2 = 167.1

P-value Approach
P-value = 0.2137
As P-value >= 0.05, fail to reject null hypothesis.

b)

Do not reject the null hypothesis

c)

There is not significant evidence that differs from 696 g. Cocaine use does not appear to affect the variation of weights