Question

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?

Data for discussion talking points

1) Diameters data frame diameters 0 2.28 1 1.26 2 1.93 3 1.38 4 2.63 5 2.11 6 2.60 7 2.20 8 2.67 9 2.92 10 2.44 11 2.13 12 1.48 13 2.56 14 2.17 15 1.90 16 1.89 17 2.27 18 2.92 19 1.87 20 2.29 21 2.18 22 3.31 23 1.96 24 2.06 25 2.71 26 2.87 27 2.22 28 2.92 29 3.14 30 1.96 31 1.70 32 2.89 33 2.30 34 1.71 35 2.74 36 3.09 37 2.92 38 2.76 39 2.13 40 2.35 41 2.20 42 2.96 43 2.50 44 3.14 45 1.96 46 3.19 47 3.01 48 2.60 49 2.11

2) 90% confidence interval (unrounded) = (2.2734912846323323, 2.506108715367667) 90% confidence interval (rounded) = ( 2.27 , 2.51 ) 99% confidence interval (unrounded) = (2.207661363228155, 2.5719386367718444) 99% confidence interval (rounded) = ( 2.21 , 2.57 )

3) z-test hypothesis test for population mean test-statistic = 1.27 two tailed p-value = 0.2046

Answer #1

The hypothesis being tested is:

H_{0}: µ = 2.30 cm

H_{a}: µ > 2.30 cm

The level of significance is 0.01.

The test statistic is 1.27.

The p-value is 0.2046/2 = 0.1023.

Since the p-value (0.1023) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the average diameter of ball bearings from the manufacturing process is greater than 2.30 cm.

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...

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.
Define the null and alternative hypothesis for this test in
mathematical terms and in words.
Report the level of significance.
INFO:
z-test hypothesis test...

Suppose that the factory claims that the proportion of ball
bearings with diameter values less than 2.20 cm in the existing
manufacturing process is the same as the proportion in the new
process. At alpha=0.05, is there enough evidence that the two
proportions are the same? Perform a hypothesis test for the
difference between two population proportions to test this
claim.
In your initial post, address the following items:
Define the null and alternative hypotheses in mathematical
terms as well...

In this discussion, you will apply the statistical concepts and
techniques covered in this week's reading about hypothesis testing
for the difference between two population proportions. In the
previous week’s discussion, you studied a manufacturing process at
a factory that produces ball bearings for automotive manufacturers.
The factory wanted to estimate the average diameter of a particular
type of ball bearing to ensure that it was being manufactured to
the factory’s specifications.
Recently, the factory began a new production line...

In this discussion, you will apply the statistical concepts and
techniques covered in this week's reading about hypothesis testing
for the difference between two population proportions. In the
previous week’s discussion, you studied a manufacturing process at
a factory that produces ball bearings for automotive manufacturers.
The factory wanted to estimate the average diameter of a particular
type of ball bearing to ensure that it was being manufactured to
the factory’s specifications.
Recently, the factory began a new production line...

Recently, the factory began a new production line that is more
efficient than the existing production line. However, the factory
still needs ball bearings to meet the same specifications. To
compare the accuracy of the new process against the existing
process, the factory decides to take two random samples of ball
bearings. The first sample is of 50 randomly selected ball bearings
from the existing production line, and the second sample is of 75
randomly selected ball bearings produced from...

The diameters of bearings used in an aircraft landing gear
assembly have a standard deviation of ? = 0.0020 cm. A random
sample of 15 bearings has an average diameter of 8.2535 cm. Please
(a) test the hypothesis that the mean diameter is 8.2500 cm using a
two-sided alternative and ? = 0.05; (b) find P-value for the test;
and (c) construct a 95% two-sided confidence interval on the mean
diameter.

The inside diameters of bearings used in an aircraft landing
gear assembly are known to have a standard deviation of ? = 0.002
cm. A random sample of 15 bearings has an average inside diameter
of 8.2535 cm. The hypothesis to be tested is that the mean inside
bearing diameter is 8.25 cm. Use a two-sided alternative and
?=0.05.
(1) Find the P-value for this test. (2) Test the hypothesis. (3)
Construct a 95% two-sided confidence interval on mean bearing...

The diameters of steel shafts produced by a certain
manufacturing process should have a mean diameter of 5.5 inches.
The diameter is known to have a standard deviation of 0.9 inches. A
random sample of 30 shafts.
(a) Find a 90% confidence interval for the mean diameter to
process.
(b) Find a 99% confidence interval for the mean diameter to
process.
(c) How does the increasing and decreasing of the significance
level affect the confidence interval? Why?
Please explain and...

This is the part of Statistics (Confidence Intervals for
Proportions and Testing Hypothesis About Proportions)
Please show and answer all the parts of this
question.
Along with interest rates, life expectancy is a component in
pricing financial annuities. Suppose that you know that last year's
average life expectancy was 77 years for your annuity holders. Now
you want to know if your clients this year have a longer life
expectancy, on average, so you randomly sample n=20 of your
recently...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 22 minutes ago

asked 28 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago