Question

A dieter believes that the average number of calories in a homemade peanut better cookie is more than the average number of calories in a store-bought peanut better cookie. which excel statements will estimate the difference in mean calories between the two types of cookies using a 90% confidence interval. the data are: homemade store-bought sample size 40 45 mean number of calories 180 179 standard deviation 2 4
a. =(180-179)+(1.96)(0.6749), and =(180-179)-(1.96)(0.6749)
b. =(180-179)+(1.645)(0.6749), and =(180-179)-(1.645)(0.6749)
c. =(45-40)+(1.96)(0.6749), and =(45-40)-(1.96)(0.6749)
d. =(45-40)+(1.645)(0.6749), and =(45-40)-(1.645)(0.6749)
e. none of the above.

Answer 1

The confidence interval formula is computed by:

Xbar ± Z s/ sqrt (n)

Where:

Xbar is the mean

Z is the z value

S is the standard deviation

N is the number of samples

 

So our given are:

90% confidence interval with a z value of 1.645

Sample size 40, 45

Mean 180, 179

Standard deviation 2, 4

 

So plugging that information in the data will give us a confidence interval:

For 1:

Xbar ± Z s/ sqrt (n)

= 180 ± 1.645 (2 / sqrt (40))

= 180 ± 1.645 (0.316227766)

= 180 ± 0.520194675

= 179.48, 180.52

For 2:

Xbar ± Z s/ sqrt (n)

= 179 ± 1.645 (4 / sqrt (45))

= 179 ± 1.645 (0.596284794)

therefore, the answer is letter b