There has been a lot of talk in recent years about the incre

There has been a lot of talk in recent years about the increased incidence of diabetes in the US population. There have been a number of arguments that it is tied to our diet of fast and processed food and our reduced lack of activity. So the Center for Disease Control collects data on the number of emergency department visits with Hypoglycemia (high blood sugar). One of the measures that they look at is the difference in visits by gender. The following data was collected: Males Females Average number of visits 141.46 155.3 Standard deviation 3.16 4.05 Sample size 24 20

a. At the 0.02 significance level, is there a difference in the variability of the admissions between males and females?

b. Given the result from part (a) on variances, test whether there is a difference in the average admissions between genders.Use a 0.01 significance level. (If you need it, the ugly degrees of freedom are 36.)

Solution

a)

H0 : var 1 = var 2

Ha: var 1 not equals var 2

Probability that var1=var2 is 0.256

As p value >0.02 accept null hypothesis.
p=0.87195 (left: 0.128; double: 0.256)

There is no significant difference between the two variances.

b)

H0: mu1 = mu2

Ha: mu1 not equals mu2.

z for 99% CI= 2.58
declare p larger than alpha=0.01 not significant.

mean1 eq: 141.46 (variance= 9.986) (se= 0.645)
mean2 eq: 155.3 (variance= 16.403) (se= 0.9056)

Difference between means:
M1-M2=141.46-155.3=-13.84
sd=6.6338; se=1.1118
99% CI of difference:
-16.7039 <-13.84< -10.9761 (Wald)
t-difference: -12.448
df-t: 35.1; p= 0 hence H0 is rejected.
(left p: 1; two sided: 0)

There is significant difference between the two means.