An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (e) O Part (d) O Part (e) What is the test statistic? (If using the z distribution round your answers two decimal places, and if using thet distribution round your answers three decimal places.) t V =L O Part () What is the p-value? O p-value < 0.010 O 0.010 0.100 Explain what the p-value means for this problem. O If Ho is false, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f H, is true, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f Ho is true, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more. O ff Ho is false, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (e) O Part (d) O Part (e) What is the test statistic? (If using the z distribution round your answers two decimal places, and if using thet distribution round your answers three decimal places.) t V =L O Part () What is the p-value? O p-value < 0.010 O 0.010 0.100 Explain what the p-value means for this problem. O If Ho is false, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f H, is true, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f Ho is true, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more. O ff Ho is false, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**Educational Website Transcription**
### Analyzing Average Time to Complete Undergraduate Degrees
An article in the *San Jose Mercury News* indicated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 years with a sample standard deviation of 1.2. The question is: Do the data support your claim at the 1% significance level?
**Note:** If you are using a Student's t-distribution for the problem, you may assume the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
#### Parts of the Problem
- **Part (a)**
- **Part (b)**
- **Part (c)**
- **Part (d)**
- **Part (e)**
#### Test Statistic
Determine the test statistic to verify the claim. If using the z distribution, round your answers to two decimal places; if using the t distribution, round your answers to three decimal places.
\[ t = \]
#### Part (f) — p-value Analysis
**What is the p-value?**
Select one:
- \( p\text{-value} < 0.010 \)
- \( 0.010 < p\text{-value} < 0.050 \)
- \( 0.050 < p\text{-value} < 0.100 \)
- \( 0.100 < p\text{-value} \)
**Explanation of the p-value for this problem:**
- **If \( H_0 \) is false,** then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
- **If \( H_0 \) is true,** then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
- **If \( H_0 \) is true,** then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
- **If \( H_0 \) is false,** then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d898972-faeb-406b-bb3a-4a7620c7739b%2F50c1489d-66a7-4015-b4d5-669f7a8c4048%2Fboo50p3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription**
### Analyzing Average Time to Complete Undergraduate Degrees
An article in the *San Jose Mercury News* indicated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 years with a sample standard deviation of 1.2. The question is: Do the data support your claim at the 1% significance level?
**Note:** If you are using a Student's t-distribution for the problem, you may assume the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
#### Parts of the Problem
- **Part (a)**
- **Part (b)**
- **Part (c)**
- **Part (d)**
- **Part (e)**
#### Test Statistic
Determine the test statistic to verify the claim. If using the z distribution, round your answers to two decimal places; if using the t distribution, round your answers to three decimal places.
\[ t = \]
#### Part (f) — p-value Analysis
**What is the p-value?**
Select one:
- \( p\text{-value} < 0.010 \)
- \( 0.010 < p\text{-value} < 0.050 \)
- \( 0.050 < p\text{-value} < 0.100 \)
- \( 0.100 < p\text{-value} \)
**Explanation of the p-value for this problem:**
- **If \( H_0 \) is false,** then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
- **If \( H_0 \) is true,** then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
- **If \( H_0 \) is true,** then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
- **If \( H_0 \) is false,** then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not
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