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 837 younger moms (less than 35 years old) and 143 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 30.67 pounds, with a standard deviation of 14.69 pounds, and the average weight gain of mature moms is 28.52 pounds, with a standard deviation of 13 pounds. Do these data provide strong evidence that there is a significant difference between the two population means

Answer 1

Answer:

From the given data, there is not enough evidence to prove that there is a statistically significant difference between the two population means

Step-by-step explanation:

The number of younger moms, in the study = 837

The average weight gain of younger moms, $\overline x$₁ = 30.67 pounds

The standard deviation of the weight gain of younger moms, s₁ = 14.69 pounds

(30.67 - 28.52)/√((14.69^2)/837 + 13²/143))

The number of younger moms, in the study = 143

The average weight gain of mature moms, $\overline x$₂ = 28.52 pounds

The standard deviation of the weight gain of mature moms, s₂ = 13 pounds

The test statistic for the difference in two populations is given as follows;

$t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_1^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}$

Therefore, we get;

$t=\dfrac{(30.67-28.52)}{\sqrt{\dfrac{14.69^{2} }{837}-\dfrac{13^{2}}{143}}} \approx 1.7919$

The test statistic ≈ (1.7919)

Using a graphing calculator, we get;

The critical-t = ±1.971379, p = 0.07459697

Therefore, given that the test statistic, (1.7919), < critical-t (0.07459697), we fail to reject the null hypothesis, therefor, the given data does not provide convincing evidence that there is a significant difference between the two population means