Question

A simple random sample of birth weights of 30 girls has a standard deviation of 829.5 hg. Use a 0.01 significance level to test the claim that birth weights of girls have the same standard deviation as the birth weights of boys, which is 660.2 hg, Assume that the population is normally distributed. Identify the following to within 2 decimal places: A The null hypothesis: i. Ho: 660.2 ii. Ho: Opt-Omer 0 iii. Ho: Ogos 2 660.2 iv. Ho: Soben v. None of the above B. Is this a one-tail or two-tail test? vi. Left-tail vii. Right-tail viii. Two-tail С. The critical values: ix. - XXR D. The test statistic: xi. Ε. The p-value of the test statistic to three decimal places: xii. p-value B 7 U HTML Editor A H

Answer 1

Answer:

a)

Option A

b)

Option C

c)

alpha = 0.01

degree of freedom = n-1 = 30 - 1 = 29

$\chi ^{2}$(df, 1-alpha/2) = 13.121

$\chi ^{2}$(df , alpha/2) = 52.336

d)

test statistic = (n-1)s^2/$\sigma$^2

substitute values

= (30-1)*829.5^2 / 660.2^2

= 45.78

e)

P value = 0.024674

= 0.025

Here we observe that, p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.