Question

5. (30 points) A group of researchers conducted a study of pregnant cocaine-dependent women. All of the women in the study used cocaine on a regular basis (at least three times a week) for more than a year. One of the many variables measured was birth-weight (in grams) of the baby delivered. Suppose a random sample of 36 cocaine-dependent women had a mean birth-weight of 2,981 grams with a standard deviation of 420 grams. Test using a 5% significance level whether the mean birth-weight is less than 3100 grams for cocaine-dependent women

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 3100
Alternative Hypothesis, Ha: μ < 3100

Rejection Region
This is left tailed test, for α = 0.05 and df = 35
Critical value of t is -1.69.
Hence reject H0 if t < -1.69

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2981 - 3100)/(420/sqrt(36))
t = -1.7

P-value Approach
P-value = 0.049
As P-value < 0.05, reject the null hypothesis.