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In this discussion, you will apply the statistical concepts and techniques covered in this week’s reading to calculate a confidence interval and perform hypothesis testing for a manufacturing process.

The manufacturing process at a factory produces ball bearings that are sold to automotive manufacturers. The factory wants to estimate the average diameter of a ball bearing that is in demand to ensure that it is manufactured within the specifications. Suppose they plan to collect a sample of 50 ball bearings and measure their diameters to construct a 90% and 99% confidence interval for the average diameter of ball bearings produced from this manufacturing process.

The sample of size 50 was generated using Python’s numpy module. This data set will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data. Check to make sure your sample data is shown in your attachment.

In your initial post, address the following items. Be sure to answer the questions about both confidence intervals and hypothesis testing.

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.

Interpret both confidence intervals. Make sure to be detailed and precise in your interpretation.

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:

Define the null and alternative hypothesis for this test in mathematical terms and in words.

Report the level of significance.

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.)

Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not?

In your follow-up posts to other students, review your peers’ calculations and provide some analysis and interpretation:

How do their confidence intervals compare with yours?

If the population standard deviation is unknown and the sample size is not sufficiently large, would you still use the Normal distribution to calculate these confidence intervals, or would you choose another distribution? If the latter, which distribution would you choose?

**note** I cant access the peers posts until I make any initial. So, provide the initial post to the prompts then I will get the peers to respond to. HTML Python script attached.

Korie Peterson posted Jul 17, 2022 11:33 AM
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When rounded to the nearest two decimal places, the 90% confidence
interval in the data is (2.37,2.61). This is showing that 90% confidence
exists with the average bearings between that given set.
When rounded to the nearest two decimal places, the 99% confidence
interval in the data is (2.31,2.67). This is showing that the average
bearings between the given set have a 99% confidence.
The bearings from the manufacturing process is µ = 2.30 cm which is
the null hypothesis. The hypothesis is right-handed because the
average of the bearings is greater based on the calculations. The
alternative hypothesis is that the average calculations of the bearings is
greater than 2.30cm.
There is a 10% chance that the bearings in the manufacturing process
is greater than 2.30cm, which means the level of significance is 10%.
The test statistic is 3.28, and the P-value is 0.001.
In my conclusion, I believe the null hypothesis should be kept since the
calculations of the bearings in the manufacturing process is 2.30 or
greater.
Seth Duck posted Jul 12, 2022 8:29 PM
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Good afternoon everyone,
1. The null statement is m>2.30 cm or that the mean is not greater
than 2.30 cm in diameter.
2. The level of significance for my test was an alpha of 0.01 or 99%
confidence level.
3. The test stat for t was 4.14 and the two tailed did not display but
is actually .000035 but we need just a single tail for this which was
.000017.
4. For this situation we can reject the hypothesis due to it being less
than the 0.01 alpha.

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