Question

A manufacturer of stone-ground deli-style mustard uses a high-speed machine to fill jars. The amount of mustard dispensed is normally distributed with a mean weight of
290 grams, and a standard deviation of 4 grams.

If the actual amounts dispensed is too low, then their customers will be cheated; if it's too high, then the company could lose money. To keep the machine properly calibrated, the company periodically takes a sample of 12 jars, to see if they need to stop production temporarily and re-calibrate. A recent sample produced a mean of 292.2 grams. Should the company be concerned that μ does not equal 290 grams? Use σ = 0:025. Use the p-value approach. (Show work)

Answer 1

Solution :

= 290

= 292.2

s = 4

n = 12

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 290

Ha : 290  

Test statistic = t

= ( - ) / s / n

= ( 292.2 -290 ) / 4 / 12

= 1.905

p(t > 1.905 ) = 1-P (t< 1.905) = 0.0832

P-value = 0.0832

= 0.025  

0.0832 < 0.025

Do not reject the null hypothesis .

There is insufficient evidence to suggest that