You work in admissions for an Intensive English Program. The program claims that its students score an average of 90 on the TOEFL. You want to evaluate this claim using a hypothesis test. You do a simple random sample of 26 students from your program and find they have a mean score of 83.9 with a standard deviation of 20. The sample has no outliers. Please write your answers to at least four decimal places. a. What will our hypotheses look like? © Ho: μ = 90 HA: 90 Ho: p = 90 HA: P 90 b. What is the standard error? c. What is the test statistic?
You work in admissions for an Intensive English Program. The program claims that its students score an average of 90 on the TOEFL. You want to evaluate this claim using a hypothesis test. You do a simple random sample of 26 students from your program and find they have a mean score of 83.9 with a standard deviation of 20. The sample has no outliers. Please write your answers to at least four decimal places. a. What will our hypotheses look like? © Ho: μ = 90 HA: 90 Ho: p = 90 HA: P 90 b. What is the standard error? c. What is the test statistic?
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![## Hypothesis Testing for Intensive English Program TOEFL Scores
### Scenario:
You work in admissions for an Intensive English Program. The program claims that its students score an average of 90 on the TOEFL.
You want to evaluate this claim using a hypothesis test. You do a simple random sample of 26 students from your program and find they have a mean score of 83.9 with a standard deviation of 20. The sample has no outliers.
Please write your answers to at least four decimal places.
### Questions:
#### a. What will our hypotheses look like?
\[
H_0: \mu = 90 \quad [selected]
\]
\[
H_A: \mu \neq 90
\]
\[
H_0: p = 90 \quad [not selected]
\]
\[
H_A: p \neq 90
\]
#### b. What is the standard error?
\[ \text{Standard Error:} \ \underline{\hspace{4cm}} \]
#### c. What is the test statistic?
\[ \text{Test Statistic:} \ \underline{\hspace{4cm}} \]
#### d. What is the p-value?
\[ \text{p-value:} \ \underline{\hspace{4cm}} \]
#### e. Based on this p-value, at a significance level of \(\alpha = 0.05\), would we reject the null hypothesis?
\[
\text{Select one:}
\]
\[
\o \ \text{Reject } H_0
\]
\[
\o \ \text{Fail to reject } H_0
\]
---
This section aims to educate students or researchers on how to conduct hypothesis testing, specifically in the context of evaluating claims about average scores within an educational program using statistical methods.
To solve the given problem, follow these steps:
1. **Formulate Hypotheses:**
- Null hypothesis (\(H_0\)): The population mean (\(\mu\)) is 90.
- Alternative hypothesis (\(H_A\)): The population mean (\(\mu\)) is not 90.
2. **Calculate Standard Error (SE):**
- Standard Error formula:
\[
SE = \frac{\text{sample standard deviation}}{\sqrt{\text{sample size}}}
\]
3. **Determine the Test Statistic:**
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8e28faf-547f-4c48-bb6d-e40546588d1c%2F515c5f6f-d098-42c6-9ca6-d3ac86062916%2Feo5r8vm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Hypothesis Testing for Intensive English Program TOEFL Scores
### Scenario:
You work in admissions for an Intensive English Program. The program claims that its students score an average of 90 on the TOEFL.
You want to evaluate this claim using a hypothesis test. You do a simple random sample of 26 students from your program and find they have a mean score of 83.9 with a standard deviation of 20. The sample has no outliers.
Please write your answers to at least four decimal places.
### Questions:
#### a. What will our hypotheses look like?
\[
H_0: \mu = 90 \quad [selected]
\]
\[
H_A: \mu \neq 90
\]
\[
H_0: p = 90 \quad [not selected]
\]
\[
H_A: p \neq 90
\]
#### b. What is the standard error?
\[ \text{Standard Error:} \ \underline{\hspace{4cm}} \]
#### c. What is the test statistic?
\[ \text{Test Statistic:} \ \underline{\hspace{4cm}} \]
#### d. What is the p-value?
\[ \text{p-value:} \ \underline{\hspace{4cm}} \]
#### e. Based on this p-value, at a significance level of \(\alpha = 0.05\), would we reject the null hypothesis?
\[
\text{Select one:}
\]
\[
\o \ \text{Reject } H_0
\]
\[
\o \ \text{Fail to reject } H_0
\]
---
This section aims to educate students or researchers on how to conduct hypothesis testing, specifically in the context of evaluating claims about average scores within an educational program using statistical methods.
To solve the given problem, follow these steps:
1. **Formulate Hypotheses:**
- Null hypothesis (\(H_0\)): The population mean (\(\mu\)) is 90.
- Alternative hypothesis (\(H_A\)): The population mean (\(\mu\)) is not 90.
2. **Calculate Standard Error (SE):**
- Standard Error formula:
\[
SE = \frac{\text{sample standard deviation}}{\sqrt{\text{sample size}}}
\]
3. **Determine the Test Statistic:**
-
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