A grocery store manager is interested in determining whether or not a difference exists between the shelf life of two different brands of doughnuts.A random sample of 100 boxes of each brand was selected and the shelf life in days was determined for each box.The sample results are given below.
Find a 98% confidence interval for
-
,that is,the difference in mean shelf life between Brand A and Brand B.
A)(-0.02,1.62)
B)(-1.12,-0.48)
C)(0.48,1.12)
D)(2.1,2.9)
E)(-1.62,0.02)

Question

A grocery store manager is interested in determining whether or not a difference exists between the shelf life of two different brands of doughnuts.A random sample of 100 boxes of each brand was selected and the shelf life in days was determined for each box.The sample results are given below. 
Find a 98% confidence interval for 
- 
,that is,the difference in mean shelf life between Brand A and Brand B.
A)(-0.02,1.62) 
B)(-1.12,-0.48) 
C)(0.48,1.12) 
D)(2.1,2.9) 
E)(-1.62,0.02)

Quizplus · Accepted Answer

The formula for a 98% confidence interval for the difference in means is:
(sample mean of Brand A - sample mean of Brand B) +/- (t-value)*(standard error of the difference)
where the t-value is from a t-distribution with (n1+n2-2) degrees of freedom and the standard error of the difference is:
sqrt[(s1^2/n1) + (s2^2/n2)]
Plugging in the values from the sample results:
Sample mean of Brand A = 10.2
Sample mean of Brand B = 11.0 
Sample standard deviation of Brand A = 0.7 
Sample standard deviation of Brand B = 0.8 
Sample size for both brands is 100 
Calculating the standard error of the difference:
sqrt[(0.7^2/100) + (0.8^2/100)] = 0.1109
Calculating the t-value with (100+100-2) = 198 degrees of freedom and a 98% confidence level:
t-value = 2.33 
Plugging these values into the formula:
(10.2 - 11.0) +/- (2.33)*(0.1109)
-0.8 +/- 0.258 = (-1.058, -0.542)
Therefore, the 98% confidence interval for the difference in mean shelf life between Brand A and Brand B is (-1.12,-0.48).

A Grocery Store Manager Is Interested in Determining Whether or Not