Discussion 3-3 Confidence Intervals and Hypothesis Testing PDF

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discussion post for module 3-3...

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1. In the Python script, you calculated the sample data to construct a 90% and 99% confidence interval for the average diameter of ball bearings produced from this manufacturing process. These confidence intervals were created using the Normal distribution based on the assumption that the population standard deviation is known, and the sample size is sufficiently large. Report these confidence intervals rounded to two decimal places. See Step 2 in the Python script. 2. Interpret both confidence intervals. Make sure to be detailed and precise in your interpretation.

The 90% confidence interval rounded to two decimal places in the sample data is (2.37, 2.61). This shows that a 90% confidence exists that the average diameter of the ball bearings is between 2.37 and 2.61. The 99% confidence interval rounded to two decimal places in the sample data is (2.31, 2.67). This shows that the average diameter of the ball bearings is between 2.31 and 2.67 with 99% confidence.

It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01. In your initial post, address the following items:

1. Define the null and alternative hypothesis for this test in mathematical terms and in words. The Null hypothesis is that the ball bearings from this manufacturing process is µ = 2.30 cm. Because there is evidence to suggest the average diameter of ball bearings from this manufacturing process is greater, the hypothesis test is right-handed. Or, the alternative hypothesis is that the average diameter of ball bearings from this manufacturing process is greater than 2.30 cm

H0 : µ = 2.30 Ha : µ > 2.30

2. Report the level of significance. The significance level is 10%. That is, there is a 10% chance that the average diameter of the ball bearings from this manufacturing process is greater than 2.30 cm.

3. Include the test statistic and the P-value. See Step 3 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.) The test-statistic is 2.42, and the P-value is .00785

4. Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not? In my analysis, the null hypothesis should be kept. This is because the average diameter of the ball bearings from this manufacturing process is 2.30 cm or greater....