Online courses: A sample of 255 students who were taking online courses were asked to describe their overall impression of online learning on a scale of 1-7, with 7 representing the most favorable impression. The average score was 5.21, and the standard deviation was 0.84. (a) Construct a 99.9% confidence interval for the mean score. (b) Assume that the mean score for students taking traditional courses is 5.47. A college that offers online courses claims that the mean scores for online courses and traditional courses are the same. Does the confidence interval contradict this claim? Explain. Part: 0 / 2 Part 1 of 2 (a) A 99.9% confidence interval for the mean score is <<. (Round the answers to at least two decimal places.)

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**Online Courses: Analysis of Student Impressions**

A study involving 255 students enrolled in online courses was conducted to evaluate their overall impression of online learning. They rated their experience on a scale from 1 to 7, with 7 indicating the most favorable view. The data gathered shows an average score of 5.21, with a standard deviation of 0.84.

**Task:**

(a) Calculate a 99.9% confidence interval for the mean score.

(b) Assume the mean score for students in traditional courses is 5.47. A college that provides online courses contends that the mean scores between online and traditional courses are equal. Determine whether the confidence interval challenges this assertion, and provide an explanation.

**Exercise:**

**Part: 0 / 2**

**Part 1 of 2**

(a) Establish a 99.9% confidence interval for the mean score: [ ] < µ < [ ].

*(Ensure to round the answers to at least two decimal places.)*
Transcribed Image Text:**Online Courses: Analysis of Student Impressions** A study involving 255 students enrolled in online courses was conducted to evaluate their overall impression of online learning. They rated their experience on a scale from 1 to 7, with 7 indicating the most favorable view. The data gathered shows an average score of 5.21, with a standard deviation of 0.84. **Task:** (a) Calculate a 99.9% confidence interval for the mean score. (b) Assume the mean score for students in traditional courses is 5.47. A college that provides online courses contends that the mean scores between online and traditional courses are equal. Determine whether the confidence interval challenges this assertion, and provide an explanation. **Exercise:** **Part: 0 / 2** **Part 1 of 2** (a) Establish a 99.9% confidence interval for the mean score: [ ] < µ < [ ]. *(Ensure to round the answers to at least two decimal places.)*
**Mortgage Rates:**

The following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day. It is reasonable to assume that the population is approximately normal.

Rates: 
- 4.752, 4.375, 4.173, 4.675, 4.421, 4.229
- 4.128, 4.250, 3.954, 4.295, 4.411

**Task:**

(a) Construct a 99% confidence interval for the mean rate. Round the answer to at least four decimal places.

- A 99% confidence interval for the mean rate is [ _ ] < μ < [ _ ].

**Submission:**

- Enter your answer in the provided input boxes.

**Instructions:**

1. Calculate the mean and standard deviation of the given rates.
2. Use the appropriate formula for the confidence interval for the mean.
3. Enter the lower and upper bounds of the confidence interval in the boxes provided.

No graphs or diagrams are included in this task description.
Transcribed Image Text:**Mortgage Rates:** The following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day. It is reasonable to assume that the population is approximately normal. Rates: - 4.752, 4.375, 4.173, 4.675, 4.421, 4.229 - 4.128, 4.250, 3.954, 4.295, 4.411 **Task:** (a) Construct a 99% confidence interval for the mean rate. Round the answer to at least four decimal places. - A 99% confidence interval for the mean rate is [ _ ] < μ < [ _ ]. **Submission:** - Enter your answer in the provided input boxes. **Instructions:** 1. Calculate the mean and standard deviation of the given rates. 2. Use the appropriate formula for the confidence interval for the mean. 3. Enter the lower and upper bounds of the confidence interval in the boxes provided. No graphs or diagrams are included in this task description.
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(a)

Obtain the 99.9% confidence interval for the mean score.

The 99.9% confidence interval for the mean score is obtained below as follows:

The formula for the Confidence interval for mean is:

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