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.

Answer 1

Solution:

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 290

Ha: 290

The test statistics,

t =( - )/ (s /n)

= ( 292.2 - 290 ) / ( 4 / 12 )

= 1.905

P-value = 0.083

The p-value is p =0.083 > 0.025, it is concluded that fail to reject the null hypothesis.

There is not sufficient evidence to claim that the company be concerned that μ does not equal 290 grams.