Question

Problem 7: The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars with mean length of at least 2.8 feet. The quality control manager wants to determine whether the production equipment needs to be adjusted. A sample of 25 bars is selected from the production line. The sample indicates a mean length of 2.73 feet, with a sample standard deviation of 0.20 feet. Should adjustments be made to the equipment? Test at the 95% confidence level.

1. State the null and alternative hypotheses.

2. Specify alpha based on the confidence level indicated.

3. Use alpha to develop the critical value that delineates the rejection region.

4. Compute the test statistic

5. Calculate P-value based on test statistic.

6. Compare the test statistic to the critical value. Compare the P-value to alpha.

7. Based on your comparisons identify your decision.

8. Indicate the conclusion for the scenario

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2.8
Alternative Hypothesis, Ha: μ ≠ 2.8

2)

0.05 is alpha

3)

Rejection Region
This is two tailed test, for α = 0.05 and df = 24
Critical value of t are -2.064 and 2.064.
Hence reject H0 if t < -2.064 or t > 2.064

4)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.73 - 2.8)/(0.2/sqrt(25))
t = -1.75

5)

P-value Approach
P-value = 0.0929

6)

As P-value >= 0.05,

7)

fail to reject null hypothesis.

8)
There is not sufficient evidence to conclude that adjustments be made to the equipment