A regulation golf ball should weigh 45 grams. A company produces golf balls for the PGA. To help ensure a high degree of accuracy, a random sample of 23 golf balls is drawn from the production line every 75 minutes and each golf ball is measured for accuracy. If the average weight of the sample is found to be significantly different than 45 grams, then the production line is shut down for inspection. The mean weight of a recent sample of 23 golf balls was found to be 47.4 grams. Use the p-value method to test the hypothesis that the mean weight of a golf ball produced by this company is different than 45 grams, using a = 0.005. Assume that the distribution of weights of all golf balls produced by this company is known to be approximately normally distributed with a standard deviation of 8.9 grams. State the null and alternative hypothesis for this test. Ho:? V H₁: ? ✓ Determine if this test is left-tailed, right-tailed, or two-tailed. Oleft-tailed O two-tailed Oright-tailed Should the standard normal (2) distribution or Student's (t) distribution be used for this test? The Student's t distribution should be used O The standard normal (2) distribution should be used Determine the test statistic for the hypothesis test. Round the solution to two decimal places. Determine the p-value for the hypothesis test. Round the solution to four decimal places.
A regulation golf ball should weigh 45 grams. A company produces golf balls for the PGA. To help ensure a high degree of accuracy, a random sample of 23 golf balls is drawn from the production line every 75 minutes and each golf ball is measured for accuracy. If the average weight of the sample is found to be significantly different than 45 grams, then the production line is shut down for inspection. The mean weight of a recent sample of 23 golf balls was found to be 47.4 grams. Use the p-value method to test the hypothesis that the mean weight of a golf ball produced by this company is different than 45 grams, using a = 0.005. Assume that the distribution of weights of all golf balls produced by this company is known to be approximately normally distributed with a standard deviation of 8.9 grams. State the null and alternative hypothesis for this test. Ho:? V H₁: ? ✓ Determine if this test is left-tailed, right-tailed, or two-tailed. Oleft-tailed O two-tailed Oright-tailed Should the standard normal (2) distribution or Student's (t) distribution be used for this test? The Student's t distribution should be used O The standard normal (2) distribution should be used Determine the test statistic for the hypothesis test. Round the solution to two decimal places. Determine the p-value for the hypothesis test. Round the solution to four decimal places.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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#27). Please show how to do test statistic and p-value.
![### Hypothesis Testing for Golf Ball Weight
A regulation golf ball should weigh 45 grams.
A company produces golf balls for the PGA. To help ensure a high degree of accuracy, a random sample of 23 golf balls is drawn from the production line every 75 minutes and each golf ball is measured for accuracy. If the average weight of the sample is found to be significantly different than 45 grams, then the production line is shut down for inspection.
The mean weight of a recent sample of 23 golf balls was found to be 47.4 grams.
Use the p-value method to test the hypothesis that the mean weight of a golf ball produced by this company is different than 45 grams, using \(\alpha = 0.005\). Assume that the distribution of weights of all golf balls produced by this company is known to be approximately normally distributed with a standard deviation of 8.9 grams.
---
#### State the Null and Alternative Hypotheses for this test
Null Hypothesis (\(H_0\)):
\[ H_0: \mu = 45 \, \text{grams} \]
Alternative Hypothesis (\(H_1\)):
\[ H_1: \mu \neq 45 \, \text{grams} \]
---
#### Determine if this test is left-tailed, right-tailed, or two-tailed.
Options:
- Left-tailed
- Two-tailed
- Right-tailed
Selection: Two-tailed
---
#### Should the standard normal (\(z\)) distribution or Student's (\(t\)) distribution be used for this test?
Options:
- The Student's \( t \) distribution should be used
- The standard normal (\(z\)) distribution should be used
Selection: The Student's \( t \) distribution should be used
---
#### Determine the test statistic for the hypothesis test. Round the solution to two decimal places.
\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]
Where:
- \(\bar{x} = 47.4\)
- \(\mu = 45\)
- \(s = 8.9\)
- \(n = 23\)
Calculate the test statistic using the above values:
\[ t = \frac{47.4 - 45}{8.9 / \sqrt{23}} \]
After calculating, the test statistic is approximately:
\[ t \approx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090c748e-ae6e-4835-a77f-8d1d8bf06681%2F3721e14c-c3d8-4e0c-8591-6e30d33da50f%2Fu4smuoj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Golf Ball Weight
A regulation golf ball should weigh 45 grams.
A company produces golf balls for the PGA. To help ensure a high degree of accuracy, a random sample of 23 golf balls is drawn from the production line every 75 minutes and each golf ball is measured for accuracy. If the average weight of the sample is found to be significantly different than 45 grams, then the production line is shut down for inspection.
The mean weight of a recent sample of 23 golf balls was found to be 47.4 grams.
Use the p-value method to test the hypothesis that the mean weight of a golf ball produced by this company is different than 45 grams, using \(\alpha = 0.005\). Assume that the distribution of weights of all golf balls produced by this company is known to be approximately normally distributed with a standard deviation of 8.9 grams.
---
#### State the Null and Alternative Hypotheses for this test
Null Hypothesis (\(H_0\)):
\[ H_0: \mu = 45 \, \text{grams} \]
Alternative Hypothesis (\(H_1\)):
\[ H_1: \mu \neq 45 \, \text{grams} \]
---
#### Determine if this test is left-tailed, right-tailed, or two-tailed.
Options:
- Left-tailed
- Two-tailed
- Right-tailed
Selection: Two-tailed
---
#### Should the standard normal (\(z\)) distribution or Student's (\(t\)) distribution be used for this test?
Options:
- The Student's \( t \) distribution should be used
- The standard normal (\(z\)) distribution should be used
Selection: The Student's \( t \) distribution should be used
---
#### Determine the test statistic for the hypothesis test. Round the solution to two decimal places.
\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]
Where:
- \(\bar{x} = 47.4\)
- \(\mu = 45\)
- \(s = 8.9\)
- \(n = 23\)
Calculate the test statistic using the above values:
\[ t = \frac{47.4 - 45}{8.9 / \sqrt{23}} \]
After calculating, the test statistic is approximately:
\[ t \approx
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