Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. In a study of the effects of prenatal cocaine use on infants, the following sample data were obtained for weights at birth: n = 193, = 2731 grams, s = 662 grams. a) Use a 0.01 significance level to test the claim that babies born to cocaine users have a mean weight that is less than the mean of 3103 grams for babies born to mothers who do not use cocaine. Claim: 3103 Ho: 3103 H1: 3103 b) What is the rejection result? Not enough information. Reject the null hypothesis. Do not reject the null hypothesis. c) What is the conclusion? Does it appear that birth weights are affected by cocaine use? There is not significant evidence that the mean is less than 3103 grams. It appears that birth weights are affected by cocaine use. There is significant evidence that the mean is less than 3103 grams. It appears that birth weights are affected by cocaine use. There is not significant evidence that the mean is less than 3103 grams. It does not appear that birth weights are affected by cocaine use. There is significant evidence that the mean is less than 3103 grams. It does not appear that birth weights are affected by cocaine use.

Answer 1

Sample size = n = 193

Sample mean = = 2731

Standard deviation = s = 662

a) Claim: babies born to cocaine users have a mean weight that is less than the mean of 3103 grams for babies born to mothers who do not use cocaine.

The null and alternative hypothesis is

Level of significance = 0.01

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 662 - 1 = 661

P-value = 0.0000

P-value value < 0.01 we rejthe ect null hypothesis.

Conclusion: There is significant evidence that the mean is less than 3103 grams. It appears that birth weights are affected by cocaine use.