A hospital wishes to justify the benefits of nutrition programs for pregnant wom

Question

A hospital wishes to justify the benefits of nutrition programs for pregnant women using birth weight data from newborns. The hospital hopes to show that the mean birth weight for newborns from mothers who complete the program is higher than the birth weight for newborns from mothers who do not complete the program. A group of 14 pregnant women were randomly divided into two groups; the first group received the nutrition program and the second group did not receive the program. The resulting weights (in grams) of the newborn babies from each group are shown below. Assume normality. a) Perform a test on variances where H_0: sigma^2_1 = sigma^2_2 versus H_a: sigma^2_1 notequalto sigma^2_2 and report your p-value to four decimal places. b) Now, assuming equal variance, let mu_1 represent the mean associated with the nutrition program, and let mu_2 represent the mean associated with no nutrition program. What are the proper hypotheses? H_0: mu_1 = mu_2 versus H_a: mu_1 notequalto mu_2 H_0: mu_1 = mu_2 versus H_a: mu_1 = mu_2 H_0: mu_1 = mu_2 versus H_a: mu_1 > mu_2 H_0: mu_1 = mu_2 versus H_a: mu_1

Explanation / Answer

a) The statistical software output for this problem is:

Two sample variance hypothesis test:
12 : Variance of Group1
22 : Variance of Group2
12/22 : Ratio of two variances
H0 : 12/22 = 1
HA : 12/22 1

Hypothesis test results:

Hence,

p - value = 0.5888

c) The statistical software output for testing of differences of mean is:

Two sample T hypothesis test:
1 : Mean of Group1
2 : Mean of Group2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 > 0
(with pooled variances)

Hypothesis test results:

Hence,

Test statistic = 1.7110

d) p - value = 0.0564

e) Option 1 is correct.

Ratio Num. DF Den. DF Sample Ratio F-Stat P-value 12/22 6 6 1.5871678 1.5871678 0.5888

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