The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads High School Grads 469 503 442 492 550 533 580 478 666 526 479 425 570 394 486 485 566 531 528 390 556 562 524 535 513 448 608 485

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The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

**College Grads:**
- 469, 503
- 550, 533
- 666, 526
- 570, 394
- 566, 531
- 556, 562
- 513, 485
- 608, 485

**High School Grads:**
- 442, 492
- 580, 478
- 479, 425
- 486, 485
- 528, 390
- 524, 535

(a) Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let μ₁ = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ₂ = population mean verbal score of students whose parents are high school graduates but do not have a college degree.)

- H₀: μ₁ - μ₂ ≥ 0  
  Hₐ: μ₁ - μ₂ < 0

- H₀: μ₁ - μ₂ = 0  
  Hₐ: μ₁ - μ₂ ≠ 0

- H₀: μ₁ - μ₂ ≤ 0  
  Hₐ: μ₁ - μ₂ > 0

- H₀: μ₁ - μ₂ ≠ 0  
  Hₐ: μ₁ - μ₂ = 0
Transcribed Image Text:The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. **College Grads:** - 469, 503 - 550, 533 - 666, 526 - 570, 394 - 566, 531 - 556, 562 - 513, 485 - 608, 485 **High School Grads:** - 442, 492 - 580, 478 - 479, 425 - 486, 485 - 528, 390 - 524, 535 (a) Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let μ₁ = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ₂ = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) - H₀: μ₁ - μ₂ ≥ 0 Hₐ: μ₁ - μ₂ < 0 - H₀: μ₁ - μ₂ = 0 Hₐ: μ₁ - μ₂ ≠ 0 - H₀: μ₁ - μ₂ ≤ 0 Hₐ: μ₁ - μ₂ > 0 - H₀: μ₁ - μ₂ ≠ 0 Hₐ: μ₁ - μ₂ = 0
### Statistical Hypothesis Testing

#### (a) Hypotheses Formulation
Select the appropriate null and alternative hypotheses for comparing two population means.

1. 
   - \( H_0: \mu_1 - \mu_2 \geq 0 \)
   - \( H_a: \mu_1 - \mu_2 < 0 \)

2. 
   - \( H_0: \mu_1 - \mu_2 \leq 0 \)
   - \( H_a: \mu_1 - \mu_2 > 0 \)

3. 
   - \( H_0: \mu_1 - \mu_2 = 0 \)
   - \( H_a: \mu_1 - \mu_2 \neq 0 \)

4. 
   - \( H_0: \mu_1 - \mu_2 < 0 \)
   - \( H_a: \mu_1 - \mu_2 = 0 \)

5. 
   - \( H_0: \mu_1 - \mu_2 = 0 \)
   - \( H_a: \mu_1 - \mu_2 > 0 \)

6. 
   - \( H_0: \mu_1 - \mu_2 \leq 0 \)
   - \( H_a: \mu_1 - \mu_2 > 0 \)

#### (b) Point Estimate
Determine the point estimate of the difference between the means for the two populations.

\[ \text{Point Estimate} = \]

#### (c) Test Statistic and p-value Calculation
Find the value of the test statistic (round your answer to three decimal places):

\[ \text{Test Statistic} = \]

Compute the p-value for the hypothesis test (round your answer to four decimal places):

\[ \text{p-value} = \]

#### (d) Conclusion at \(\alpha = 0.05\)
Based on the p-value and significance level, what is your conclusion?

1. 
   - Do not reject \( H_0 \). There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

2. 
   - Do not reject \( H_0 \). There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

3.
Transcribed Image Text:### Statistical Hypothesis Testing #### (a) Hypotheses Formulation Select the appropriate null and alternative hypotheses for comparing two population means. 1. - \( H_0: \mu_1 - \mu_2 \geq 0 \) - \( H_a: \mu_1 - \mu_2 < 0 \) 2. - \( H_0: \mu_1 - \mu_2 \leq 0 \) - \( H_a: \mu_1 - \mu_2 > 0 \) 3. - \( H_0: \mu_1 - \mu_2 = 0 \) - \( H_a: \mu_1 - \mu_2 \neq 0 \) 4. - \( H_0: \mu_1 - \mu_2 < 0 \) - \( H_a: \mu_1 - \mu_2 = 0 \) 5. - \( H_0: \mu_1 - \mu_2 = 0 \) - \( H_a: \mu_1 - \mu_2 > 0 \) 6. - \( H_0: \mu_1 - \mu_2 \leq 0 \) - \( H_a: \mu_1 - \mu_2 > 0 \) #### (b) Point Estimate Determine the point estimate of the difference between the means for the two populations. \[ \text{Point Estimate} = \] #### (c) Test Statistic and p-value Calculation Find the value of the test statistic (round your answer to three decimal places): \[ \text{Test Statistic} = \] Compute the p-value for the hypothesis test (round your answer to four decimal places): \[ \text{p-value} = \] #### (d) Conclusion at \(\alpha = 0.05\) Based on the p-value and significance level, what is your conclusion? 1. - Do not reject \( H_0 \). There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. 2. - Do not reject \( H_0 \). There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. 3.
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