Marijuana Use During Pregnancy. To study the effects of marijuana use during pre

Question

Marijuana Use During Pregnancy.
To study the effects of marijuana use during pregnancy the birth weights of babies that were born to mothers who used marijuana during their pregnancy and birth weights of babies born to mother who did not use marijuana during pregnancy were collected. The difference in the average birth weight of nonuser mothers minus user mothers was computed to be 280 g. The standard error of the difference was 46.66 g with 85 degrees of freedom.

a. Test whether there is a difference in mean birth weight of babies born to mothers who didn’t use marijuana compared to those that did use marijuana at = 0.05.

b. Construct a 95% confidence interval for the difference in mean birth weight of babies whose mothers didn’t use marijuana and those that did.

Explanation / Answer

a. Test whether there is a difference in mean birth weight of babies born to mothers who didn’t use marijuana compared to those that did use marijuana at = 0.05.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 and u2 are two population mean birth weight of babies born to mothers who didn’t use marijuana compared to those that did use marijuana.

Assume alpha= level of significance = 0.05

Also given that,

X1bar - X2bar = 280 g

SE = 46.66 g

df = 85

The test statistic is,

t = (X1bar - X2bar) / SE

t = 280 / 46.66 = 6.00

Now we have to find p-value for taking decision.

P-value we can find in EXCEL.

syntax :

=TDIST(x, deg_freedom, tails)

where x is absolute value of test statistic.

deg_freedom = 85

tails = 2

P-value = 4.67765E-08 = 0.000

P-value <alpha

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that there is a difference in mean birth weight of babies born to mothers who didn’t use marijuana compared to those that did use marijuana.

b. Construct a 95% confidence interval for the difference in mean birth weight of babies whose mothers didn’t use marijuana and those that did.

95% confidence interval for difference in mean is,

(X1bar - X2bar) - E < mu1-mu2 < (X1bar + X2bar) + E

where E is margin of error.

E = tc*SE

tc is critical value fo t-distribution.

tc we can find in EXCEL.

syntax:

=TINV(probability, deg_freedom)

where probability = 0.05

deg_freedom = 85

tc= 1.988

E = 1.988*46.66 = 92.76

95% confidence interval for mu1-mu2 is,

280 - 92.76 < mu1 - mu2 < 280 + 92.76

187.24 < mu1-mu2 < 372.76

95% confidence interval for the difference in mean birth weight of babies whose mothers didn’t use marijuana and those that did is (187.24, 372.76).

We are 95% confident that the the difference in mean birth weight of babies whose mothers didn’t use marijuana and those that did is lies between 187.24 and 372.76.

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