Question

The inside diameters of bearings used in an aircraft landing gear assembly is known to have a standard deviation of s = 0.002 cm. A random sample of 15 bearings has an average inside diameter of 8.2535 cm. (a) Test the hypothesis that the mean inside bearing diameter is 8.25 cm. Use a two-sided alternative and a = 0.05.

Answer 1

To test the hypothesis that the mean inside bearing diameter is 8.25 cm, perform a hypothesis test and compare the test statistic to the critical value

Step-by-step explanation:

To test the hypothesis that the mean inside bearing diameter is 8.25 cm, we need to perform a hypothesis test.

Step 1: Define the null and alternative hypotheses:
Null Hypothesis (H0): The mean inside bearing diameter is 8.25 cm.
Alternative Hypothesis (Ha): The mean inside bearing diameter is not equal to 8.25 cm.

Step 2: Set the significance level (α) at 0.05.

Step 3: Calculate the test statistic:
T-test = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(n))

Step 4: Determine the critical value(s) based on the significance level and degrees of freedom.

Step 5: Compare the test statistic to the critical value(s) and make a decision whether to reject or fail to reject the null hypothesis.

Step 6: State the conclusion based on the decision.