Two professors at a local college developed a new teaching currículum designed to increase students' grades in math classes. In a typical developmental math course, 51% of the students complete the course With a letter grade of A, B I the experimental course, of the 18 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a 0.05 level of significance? Complete parts (a) through (g) (a) State the appropriate null and alternative hypotheses. Ho: P- 0.51 versus Hy: P> 0.51 (Type integers or decimals. Do not round.) (b) Verify that the normal model may not be used estimate the P-value. Because npo (1-Po) -4.5 > 10, the normal model may not be used to approximate the P-value. (Round to one decimal place as neoded.) (c) Explain why this is a binomial experiment. are independent and the probability of success is fixed at 0.51 for each trial. There is a fixed number of trials with two mutually exclusive outcomes. (Type an integer or a decimal. Do not round.) The trials (d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test.
Two professors at a local college developed a new teaching currículum designed to increase students' grades in math classes. In a typical developmental math course, 51% of the students complete the course With a letter grade of A, B I the experimental course, of the 18 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a 0.05 level of significance? Complete parts (a) through (g) (a) State the appropriate null and alternative hypotheses. Ho: P- 0.51 versus Hy: P> 0.51 (Type integers or decimals. Do not round.) (b) Verify that the normal model may not be used estimate the P-value. Because npo (1-Po) -4.5 > 10, the normal model may not be used to approximate the P-value. (Round to one decimal place as neoded.) (c) Explain why this is a binomial experiment. are independent and the probability of success is fixed at 0.51 for each trial. There is a fixed number of trials with two mutually exclusive outcomes. (Type an integer or a decimal. Do not round.) The trials (d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![Two professors at a local college developed a new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 51% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 18 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the α = 0.05 level of significance? Complete parts (a) through (g).
(a) State the appropriate null and alternative hypotheses.
- \( H_0: p = 0.51 \) versus \( H_1: p > 0.51 \)
(Type integers or decimals. Do not round.)
(b) Verify that the normal model may not be used to estimate the P-value.
- Because \( np_0 (1 - p_0) = 4.5, > 10 \), the normal model **may not** be used to approximate the P-value.
(Round to one decimal place as needed.)
(c) Explain why this is a binomial experiment.
- There is a **fixed** number of trials with **two mutually exclusive outcomes**. The trials **are** independent and the probability of success is fixed at \( 0.51 \) for each trial.
(Type an integer or a decimal. Do not round.)
(d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test.
- First determine the P-value.
- P-value = [ ] (Round to three decimal places as needed.)
Is there sufficient evidence to support the research that the experimental course is effective?
- O A. No, reject the null hypothesis because the P-value is less than α. There is insufficient evidence to conclude that the experimental course is effective.
- O B. Yes, reject the null hypothesis because the P-value is less than α. There is sufficient evidence to conclude that the experimental course is effective.
- O C. Yes, do not reject the null hypothesis because the P-value is greater than α. There is sufficient evidence to conclude that the experimental course is effective.
- O D. No, do not reject the null hypothesis because the P-value is greater than α. There is insufficient evidence to conclude that the experimental course is effective.
(e) Suppose the course is taught with 54 students and 39 complete the course with a letter grade of A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77aea7c1-e1b0-47d1-a611-3ed1fc1f706d%2Fd21303dc-d199-49eb-9f21-951609abd03c%2Ffefcri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Two professors at a local college developed a new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 51% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 18 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the α = 0.05 level of significance? Complete parts (a) through (g).
(a) State the appropriate null and alternative hypotheses.
- \( H_0: p = 0.51 \) versus \( H_1: p > 0.51 \)
(Type integers or decimals. Do not round.)
(b) Verify that the normal model may not be used to estimate the P-value.
- Because \( np_0 (1 - p_0) = 4.5, > 10 \), the normal model **may not** be used to approximate the P-value.
(Round to one decimal place as needed.)
(c) Explain why this is a binomial experiment.
- There is a **fixed** number of trials with **two mutually exclusive outcomes**. The trials **are** independent and the probability of success is fixed at \( 0.51 \) for each trial.
(Type an integer or a decimal. Do not round.)
(d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test.
- First determine the P-value.
- P-value = [ ] (Round to three decimal places as needed.)
Is there sufficient evidence to support the research that the experimental course is effective?
- O A. No, reject the null hypothesis because the P-value is less than α. There is insufficient evidence to conclude that the experimental course is effective.
- O B. Yes, reject the null hypothesis because the P-value is less than α. There is sufficient evidence to conclude that the experimental course is effective.
- O C. Yes, do not reject the null hypothesis because the P-value is greater than α. There is sufficient evidence to conclude that the experimental course is effective.
- O D. No, do not reject the null hypothesis because the P-value is greater than α. There is insufficient evidence to conclude that the experimental course is effective.
(e) Suppose the course is taught with 54 students and 39 complete the course with a letter grade of A
Transcribed Image Text:**Title: Analyzing the Effectiveness of a New Teaching Curriculum**
**Context:**
Two professors at a local college developed a curriculum to enhance students’ math grades. In a standard course, 51% of students typically earn an A, B, or C. For the experimental course, 13 out of 18 enrolled students received these grades. The goal is to evaluate the curriculum's effectiveness using a 0.05 significance level.
**Decision:**
- **Option C:** Yes, do not reject the null hypothesis; the P-value exceeds alpha (α), implying insufficient evidence that the experimental course is effective.
- **Option D:** No, do not reject the null hypothesis; the P-value exceeds alpha (α), indicating insufficient evidence to confirm the effectiveness of the course.
**Parameters for Normal Model:**
(e) The course, now with 54 students and 39 achieving grades A, B, or C, requires a check on suitable conditions for using the normal model for P-value estimation:
- Required: np₀(1 - p₀) = 13.5 ≥ 10
- Sample size: less than 5% of the population
- Sample: can reasonably be assumed random
- Normal model application: may be suitable
**Hypothesis Test:**
(f) Calculating and interpreting P-value using the normal model:
- Test statistic, z₀: (To be rounded)
- P-value: (To be rounded)
**Conclusion:**
- **Option A:** Reject null hypothesis; P-value < α. Course is likely effective.
- **Option B:** Do not reject null hypothesis; P-value > α. Insufficient evidence.
- **Option C:** Do not reject; P-value < α. Insufficient evidence.
- **Option D:** Do not reject; P-value > α. Insufficient evidence.
**Sample Size Impact:**
(g) Role of sample size in hypothesis testing:
- Smaller sample sizes may lead to substantial evidence absent to reject null hypothesis. Larger studies are advised before drawing conclusive evidence with small samples.
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