b. Now suppose the sample consists of 30 boys instead of 15 and repeat the test. Find the test statistic. t= (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. p= (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject Ho. Choose the correct answer below. O A. Reject Ho. There is reason to believe that 37 in. is not the population mean at a significance level of 0.05. O B. Do not reject Ho. The population mean is definitely 37 in. on the basis of these data at a significance level of 0.05. C. Do not reject Ho. There is no reason to believe that 37 in. is not the population mean at a significance level of 0.05. O D. Reject Ho. The population mean is definitely not 37 in. on the basis of these data at a significance level of 0.05. c. Explain why the t-values and p-values for parts a and b are different. Choose the correct answer below. O A. A larger n causes a larger standard error (wider sampling distribution) with more area in the tails, as shown by the larger p-value. B. A larger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the larger p-value. C. A larger n causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value. D. A larger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the
b. Now suppose the sample consists of 30 boys instead of 15 and repeat the test. Find the test statistic. t= (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. p= (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject Ho. Choose the correct answer below. O A. Reject Ho. There is reason to believe that 37 in. is not the population mean at a significance level of 0.05. O B. Do not reject Ho. The population mean is definitely 37 in. on the basis of these data at a significance level of 0.05. C. Do not reject Ho. There is no reason to believe that 37 in. is not the population mean at a significance level of 0.05. O D. Reject Ho. The population mean is definitely not 37 in. on the basis of these data at a significance level of 0.05. c. Explain why the t-values and p-values for parts a and b are different. Choose the correct answer below. O A. A larger n causes a larger standard error (wider sampling distribution) with more area in the tails, as shown by the larger p-value. B. A larger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the larger p-value. C. A larger n causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value. D. A larger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
B please and thank you
![**Analysis of Hypothesis Testing with a Larger Sample Size**
**Situation:**
Suppose the sample consists of 30 boys instead of 15, and the test is repeated.
1. **Calculate the Test Statistic:**
- \( t = \) [Type an integer or decimal rounded to two decimal places as needed.]
2. **Determine the p-value:**
- \( p = \) [Type an integer or decimal rounded to three decimal places as needed.]
**Decision Making:**
- Reject or do not reject \( H_0 \). Choose the correct answer below:
- **A.** Reject \( H_0 \). There is reason to believe that 37 in. is not the population mean at a significance level of 0.05.
- **B.** Do not reject \( H_0 \). The population mean is definitely 37 in. on the basis of these data at a significance level of 0.05.
- **C.** Do not reject \( H_0 \). There is no reason to believe that 37 in. is not the population mean at a significance level of 0.05.
- **D.** Reject \( H_0 \). The population mean is definitely not 37 in. on the basis of these data at a significance level of 0.05.
**Understanding the Differences in t-values and p-values:**
Why are the t-values and p-values for parts a and b different? Choose the correct answer below:
- **A.** A larger \( n \) causes a larger standard error (wider sampling distribution) with more area in the tails, as shown by the larger p-value.
- **B.** A larger \( n \) causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the larger p-value.
- **C.** A larger \( n \) causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value.
- **D.** A larger \( n \) causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the smaller p-value.
This educational segment helps in understanding how changes in sample size can affect the outcome and interpretation of hypothesis tests.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24cab7c0-6f2e-4f27-9ff2-6438353b4e66%2F0b4dec63-87f9-4686-9b5f-d61fe63a9bc9%2Fd7fff0q_processed.png&w=3840&q=75)
Transcribed Image Text:**Analysis of Hypothesis Testing with a Larger Sample Size**
**Situation:**
Suppose the sample consists of 30 boys instead of 15, and the test is repeated.
1. **Calculate the Test Statistic:**
- \( t = \) [Type an integer or decimal rounded to two decimal places as needed.]
2. **Determine the p-value:**
- \( p = \) [Type an integer or decimal rounded to three decimal places as needed.]
**Decision Making:**
- Reject or do not reject \( H_0 \). Choose the correct answer below:
- **A.** Reject \( H_0 \). There is reason to believe that 37 in. is not the population mean at a significance level of 0.05.
- **B.** Do not reject \( H_0 \). The population mean is definitely 37 in. on the basis of these data at a significance level of 0.05.
- **C.** Do not reject \( H_0 \). There is no reason to believe that 37 in. is not the population mean at a significance level of 0.05.
- **D.** Reject \( H_0 \). The population mean is definitely not 37 in. on the basis of these data at a significance level of 0.05.
**Understanding the Differences in t-values and p-values:**
Why are the t-values and p-values for parts a and b different? Choose the correct answer below:
- **A.** A larger \( n \) causes a larger standard error (wider sampling distribution) with more area in the tails, as shown by the larger p-value.
- **B.** A larger \( n \) causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the larger p-value.
- **C.** A larger \( n \) causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value.
- **D.** A larger \( n \) causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the smaller p-value.
This educational segment helps in understanding how changes in sample size can affect the outcome and interpretation of hypothesis tests.
![### Hypothesis Testing for Population Mean Differences
**Context:**
In Country A, the population mean height for 3-year-old boys is 37 inches. A sample of 15 boys from Country B shows a mean height of 36.2 inches with a standard deviation of 3 inches. Assuming heights are Normally distributed, we aim to determine if the mean height in Country B is significantly different from Country A using a significance level of 0.05.
**a. Hypothesis Testing:**
**Objective:**
Determine if the mean for Country B is significantly different from Country A.
**Choose the Correct Hypotheses:**
1. \( H_0: \mu \geq 37 \) vs \( H_a: \mu < 37 \)
2. \( H_0: \mu = 37 \) vs \( H_a: \mu < 37 \)
3. \( H_0: \mu > 37 \) vs \( H_a: \mu \leq 37 \)
4. \( H_0: \mu = 37 \) vs \( H_a: \mu \neq 37 \)
5. \( H_0: \mu = 37 \) vs \( H_a: \mu > 37 \)
6. \( H_0: \mu \neq 37 \) vs \( H_a: \mu = 37 \)
**Calculate the Test Statistic:**
\[ t = \, \] (Type an integer or decimal rounded to two decimal places as needed.)
**Calculate the p-value:**
\[ p = \, \] (Type an integer or decimal rounded to three decimal places as needed.)
**Decision:**
Choose the correct decision based on the significance level of 0.05:
1. Reject \( H_0 \). The population mean is definitely not 37 in. based on these data.
2. Reject \( H_0 \). There is reason to believe that 37 in. is not the population mean.
3. Do not reject \( H_0 \). There is no reason to believe that 37 in. is not the population mean.
4. Do not reject \( H_0 \). The population mean is definitely 37 in. at the significance level.
*Note: Fill in the values for the test statistic and p-value after performing calculations.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24cab7c0-6f2e-4f27-9ff2-6438353b4e66%2F0b4dec63-87f9-4686-9b5f-d61fe63a9bc9%2Fadnfj69_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Population Mean Differences
**Context:**
In Country A, the population mean height for 3-year-old boys is 37 inches. A sample of 15 boys from Country B shows a mean height of 36.2 inches with a standard deviation of 3 inches. Assuming heights are Normally distributed, we aim to determine if the mean height in Country B is significantly different from Country A using a significance level of 0.05.
**a. Hypothesis Testing:**
**Objective:**
Determine if the mean for Country B is significantly different from Country A.
**Choose the Correct Hypotheses:**
1. \( H_0: \mu \geq 37 \) vs \( H_a: \mu < 37 \)
2. \( H_0: \mu = 37 \) vs \( H_a: \mu < 37 \)
3. \( H_0: \mu > 37 \) vs \( H_a: \mu \leq 37 \)
4. \( H_0: \mu = 37 \) vs \( H_a: \mu \neq 37 \)
5. \( H_0: \mu = 37 \) vs \( H_a: \mu > 37 \)
6. \( H_0: \mu \neq 37 \) vs \( H_a: \mu = 37 \)
**Calculate the Test Statistic:**
\[ t = \, \] (Type an integer or decimal rounded to two decimal places as needed.)
**Calculate the p-value:**
\[ p = \, \] (Type an integer or decimal rounded to three decimal places as needed.)
**Decision:**
Choose the correct decision based on the significance level of 0.05:
1. Reject \( H_0 \). The population mean is definitely not 37 in. based on these data.
2. Reject \( H_0 \). There is reason to believe that 37 in. is not the population mean.
3. Do not reject \( H_0 \). There is no reason to believe that 37 in. is not the population mean.
4. Do not reject \( H_0 \). The population mean is definitely 37 in. at the significance level.
*Note: Fill in the values for the test statistic and p-value after performing calculations.*
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