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 = 195,  = 2600 grams, s = 621 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:   ---Select--- < > ≥ ≤ ≠ = 3103

H_o:     ---Select--- < > ≥ ≤ ≠ = 3103

H₁:     ---Select--- < > ≥ ≤ ≠ = 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

(a) Ho: = 3103

Ha: < 3103

(b) n = 195

sample man = 2600

sample sd = 621

Assuming that the data is normally distributed, also as the population sd is not given, we will calculate t ststaistics

  

The t-critical value for a left-tailed test, for a significance level of α=0.01

tc = −2.346

As the t stat falls in the rejection area, we reject the Null hypothesis.

(c)

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