Question

Weight gain during pregnancy. In 2004, the state of North Carolina released to the public a large data set containing information on births recorded in this state. This data set has been of interest to medical researchers who are studying the relationship between habits and practices of expectant mothers and the birth of their children. The following histograms show the distributions of weight gain during pregnancy by 842 younger moms (less than 35 years old) and 144 mature moms (35 years old and over) who have been randomly sampled from this large data set. The average weight gain of younger moms is 30.91 pounds, with a standard deviation of 14.57 pounds, and the average weight gain of mature moms is 29.25 pounds, with a standard deviation of 13.23 pounds. Do these data provide strong evidence that there is a significant difference between the two population means? Conduct a hypothesis test.

Note: The degrees of freedom for this problem is df = 206.96028. Round all results to 4 decimal places. Remember not to round for intermediate calculations!

1. Which set of hypotheses should the researcher use?
A. ?0H0: ?1−?2=0p1−p2=0, ??HA: ?1−?2≠0p1−p2≠0
B. ?0H0: ?1−?2=0μ1−μ2=0, ??HA: ?1−?2>0μ1−μ2>0
C. ?0H0: ?1−?2=0p1−p2=0, ??HA: ?1−?2<0p1−p2<0
D. ?0H0: ?1−?2=0μ1−μ2=0, ??HA: ?1−?2≠0μ1−μ2≠0

2. Calculate the test statistic.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.  
p value =

4. Suppose that a researcher today decides to replicate this study. Using the information from the 2004 study, they calculate an effect size of 0.12. Next, they obtain a new sample of 124 younger moms and a new sample of 86 mature moms and, using their new sample data, conduct the same hypothesis test. They calculate a p-value of 0.2191 and an effect size of 0.124. Does their new study confirm or conflict with the study from 2004?
A. The researcher cannot make a comparison because the sample sizes are not the same.
B. It confirms the 2004 study because the sample of moms from today is independent of the sample of moms from 2004.
C. It contradicts the 2004 study because the p-value is larger.
D. It contradicts the 2004 study because the effect sizes are not exactly the same.
E. It confirms the 2004 study because the effect sizes are nearly the same.

Answer 1

1) The null and alternative hypothesis

A)

2) Test statistic

= 1.66/1.2115

= 1.3702

Note : This is a t test for unequal variance

3) Pvalue = P( t<-1.3002 ) +P( t> 1.3702)

Note : as the test is two tailed , P value is calculated for two tails

P value = 0.0861

Note : degrees of freedom = 207

Note : Excel formula for P value "=T.DIST.2T(t=1.3702,df=207)"

4) Answer is

E) It confirms the 2004 study as the effect sizes are nearly the same