Question

You’re a quality control engineer for Norman’s fourth largest cracker factory, and you plan to implement some process changes if you conclude that the mean weight of a 32 ounce box of saltine crackers is less than 32 ounces. Based on a sample of 15 boxes, you found an average and standard deviation of cracker box weight of 31.6 ounces and 1.2 ounces, respectively.

a. Draw conclusions with the critical value approach at 99% confidence.

b. What is the probability that you conclude that no process changes are needed when the actual mean box weight is 31.7 ounces? Use the table in the textbook.

c. Redo part b, but instead use Excel.

Answer 1

Here sample size n is less than 30. so we do use t-test

t =(x' - U)/sd/sqrt(n) where

Mean x' = 31.6

Population mean U=32

Sd = 1.2

sample size n = 15

We find the value of t-test statistic is

t=(x'-U)/S/sqrt(n)

=> t = (31.6 - 32) / (1.2/sqrt(15)

=> -1.2910

|t|=-1.2910

For 99% CI, P = 0.005 +0.99 + 0.005 = 0.99 only ehich is (0.005) only

df = n - 1 = 15 -1 = 14

to solve in Excel sheet we use =TINV(probability, degrees of freedom)

by substitution here...

we get like..

Finally Command is =TINV(0.005,14) then Press Enter Key in Excel

Critical value of t = 3.3256 (Use 4 decimal place)

calculated value of t = 1.2910 <   critical value of t = 3.3256

We can accept the null hypothesis Ho.