The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 9 processing times from computer 1 showed a mean of 72 seconds with a standard deviation of 19 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 61 seconds with a standard deviation of 20 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that the mean processing time of computer 1, H, is greater than the mean processing time of computer 2, H? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. H, :0 H¡ :0 믐 (b) Determine the type of test statistic to use. (Choose one) ▼ OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean processing time of computer 1 is greater than the mean processing time of computer 2? O Yes ONo
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 9 processing times from computer 1 showed a mean of 72 seconds with a standard deviation of 19 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 61 seconds with a standard deviation of 20 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that the mean processing time of computer 1, H, is greater than the mean processing time of computer 2, H? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. H, :0 H¡ :0 믐 (b) Determine the type of test statistic to use. (Choose one) ▼ OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean processing time of computer 1 is greater than the mean processing time of computer 2? O Yes ONo
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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![**Hypothesis Test for the Difference of Population Means: t-test**
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require comparable processing time to those of computer 2. A random sample of 9 processing times from computer 1 showed a mean of 72 seconds with a standard deviation of 19 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 61 seconds with a standard deviation of 20 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that the mean processing time of computer 1, μ₁, is greater than the mean processing time of computer 2, μ₂?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\).
\(H_0:\) [ ]
\(H_1:\) [ ]
(b) Determine the type of test statistic to use.
(Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.) [ ]
(d) Find the \(p\)-value. (Round to three or more decimal places.) [ ]
(e) Can we conclude that the mean processing time of computer 1 is greater than the mean processing time of computer 2?
○ Yes ○ No
---
**Graph/Diagram Explanation:**
To the right, there is a panel containing various statistical symbols and notations commonly used in hypothesis testing, including:
- Mean (\(\mu\))
- Standard deviation (\(\sigma\))
- Probability (\(P\))
- Sample mean (\(\bar{x}\))
- Sample standard deviation (\(S\))
- Population proportion (\(\hat{P}\))
- Various mathematical and statistical operators and symbols.
These symbols and operators are used in formulating and solving the steps involved in the hypothesis test.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F438f9e3e-5163-4042-928f-6af00166f2ed%2F6f6f1e93-9796-4690-8ead-ee44ff511c5e%2Fehqt46p_processed.png&w=3840&q=75)
Transcribed Image Text:**Hypothesis Test for the Difference of Population Means: t-test**
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require comparable processing time to those of computer 2. A random sample of 9 processing times from computer 1 showed a mean of 72 seconds with a standard deviation of 19 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 61 seconds with a standard deviation of 20 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that the mean processing time of computer 1, μ₁, is greater than the mean processing time of computer 2, μ₂?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\).
\(H_0:\) [ ]
\(H_1:\) [ ]
(b) Determine the type of test statistic to use.
(Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.) [ ]
(d) Find the \(p\)-value. (Round to three or more decimal places.) [ ]
(e) Can we conclude that the mean processing time of computer 1 is greater than the mean processing time of computer 2?
○ Yes ○ No
---
**Graph/Diagram Explanation:**
To the right, there is a panel containing various statistical symbols and notations commonly used in hypothesis testing, including:
- Mean (\(\mu\))
- Standard deviation (\(\sigma\))
- Probability (\(P\))
- Sample mean (\(\bar{x}\))
- Sample standard deviation (\(S\))
- Population proportion (\(\hat{P}\))
- Various mathematical and statistical operators and symbols.
These symbols and operators are used in formulating and solving the steps involved in the hypothesis test.
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