both pictures are one problem 2. For the 500 women with GDM that you sampled for

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both pictures are one problem

2. For the 500 women with GDM that you sampled for your study, you also found that 70% were overweight or obese, and 30% were norrmal weight prior to pregnancy. The data you collected on these women also includes fasting glucose measured within 3 months prior to pregnancy. The mean ± SD fasting glucose for overweight/obese women is 102.1 ± 20.0 mg/dL, and 98.8 ± 16.0 mg/dL for normal weight women. a. Determine whether the mean ± SD fasting glucose prior to pregnancy is significantly different for overweight/obese women compared to normal weight women, at a 5% significance level. Show all work. If the precise DF you need is not given in the table, use the closest DF available in the table. (18 pts) Hypotheses Test Statistic: Critical Value: Answer: Conclusion

Explanation / Answer

Question 2

Part a

Here, we have to use two sample t test for the population mean. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no any statistically significant difference for the average glucose prior to pregnancy for overweight/obese women and normal weight women.

Alternative hypothesis: Ha: There is a statistically significant difference for the average glucose prior to pregnancy for overweight/obese women and normal weight women.

H0: µ1 = µ2 versus Ha: µ1 µ2

This is a two tailed test.

Test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]

We are given

X1bar = 102.1

X2bar = 98.8

S1 = 20

S2 = 16

N1 = 500*0.70 = 350

N2 = 500*0.30 = 150

Level of significance = alpha = = 0.05 = 5%

Degrees of freedom = 500 – 2 = 498

Critical values = -1.9647 and 1.9647

Test statistic = t = (102.1 - 98.8) / sqrt((20^2/350)+(16^2/150))

Test statistic = t = 1.954914621

P-value = 0.0512

= 0.05

P-value >

So, we do not reject the null hypothesis that there is no any statistically significant difference for the average glucose prior to pregnancy for overweight/obese women and normal weight women.

There is insufficient evidence to conclude that there is a statistically significant difference for the average glucose prior to pregnancy for overweight/obese women and normal weight women.

Part b

Here, we have to use two sample t test for the population mean. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no any statistically significant difference for the average glucose prior to pregnancy for overweight/obese women and normal weight women.

Alternative hypothesis: Ha: The average glucose prior to pregnancy for overweight/obese women is higher than average glucose prior to pregnancy for normal weight women.

H0: µ1 = µ2 versus Ha: µ1 > µ2

This is a one tailed test. This is an upper tailed test. This is right tailed test.

Test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]

We are given

X1bar = 102.1

X2bar = 98.8

S1 = 20

S2 = 16

N1 = 500*0.70 = 350

N2 = 500*0.30 = 150

Level of significance = alpha = = 0.05 = 5%

Degrees of freedom = 500 – 2 = 498

Upper Critical values = 1.6479

Test statistic = t = (102.1 - 98.8) / sqrt((20^2/350)+(16^2/150))

Test statistic = t = 1.954914621

P-value = 0.0256

= 0.05

P-value <

So, we reject the null hypothesis that there is no any statistically significant difference for the average glucose prior to pregnancy for overweight/obese women and normal weight women.

There is sufficient evidence to conclude that the average glucose prior to pregnancy for overweight/obese women is higher than average glucose prior to pregnancy for normal weight women.

Part c

Second analysis b had greater power because the p-value for part b is less than part a.

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