Question

A process has a mean of 40 grams and standard deviation of 2 grams. With a 90% of confidence level, determine is the mean was reduced. Samples: 38, 39, 42, 40, 39, 41, 42, 40, 41, 42. Determine the 5 steps and p value of the hypothesis test.

Step 1: Ho: μ = 40 grams H1: μ < 40 grams

Step 2: Normal Distribution

Step 3: Critical Value : -1.28

Step 4: Experimental Value: 0.63

Step 5: Ho is accepted, or Ho is not rejected, or H1 is rejected.

Step 6: P value = 0.735653

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 40
Alternative Hypothesis, Ha: μ < 40

Normal distribution

Rejection Region
This is left tailed test, for α = 0.1
Critical value of z is -1.28.
Hence reject H0 if z < -1.28

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (40.4 - 40)/(2/sqrt(10))
z = 0.63

P-value Approach
P-value = 0.735653
As P-value >= 0.1, fail to reject null hypothesis.