This question is incomplete, the complete question is;
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 amount 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 ≠ 290 grams? Use σ = 0:025. Use the p-value approach.
Answer:
P-Value = 0.08324
p-value ( 0.08324 ) is greater than significance level σ ( 0.025 );
fail to reject the null hypothesis
the company should not be concerned because, we have sufficient evidence to conclude that the mean weight is not different from 290 grams.
Step-by-step explanation:
Given the data in the question;
mean weight μ = 290 grams
sample mean x" = 292.2 grams
standard deviation s= 4 grams
sample size n = 12 jars
degree of freedom DF = n - 1 = 12 - 1 = 11
significance level σ = 0.025
Two tailed Test
Null hypothesis H₀ : μ = 290
Alternative hypothesis Hₐ : μ ≠ 290
Test Statistics;
t = ( x" - μ ) / ( s/√n )
we substitute our values into the equation
t = ( 292.2 - 290 ) / ( 4/√12 )
t = 2.2 / 1.1547
t = 1.905
From table; { t=1.905, df = 11, } Two tailed
P-Value = 0.08324
Hence, p-value ( 0.08324 ) is greater than significance level σ ( 0.025 );
fail to reject the null hypothesis meaning μ = 290
So the company should not be concerned because, we have sufficient evidence to conclude that the mean weight is not different from 290 grams.
