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. The confidence intervals rounded to two decimal places are: 90%= ( 2.40, 2.64) and 99% = (2.34, 2.70) 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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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. The confidence intervals rounded to two decimal places are: 90%= ( 2.40, 2.64) and 99% = (2.34, 2.70)

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?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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