nfidence interval

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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### Confidence Intervals for Population Means

#### Challenge Activity: 5.7.1 Confidence Intervals for Population Means

**Scenario:**

Suppose the mean height in inches of all 9th-grade students at one high school is estimated. The population standard deviation is 3 inches. The heights of 8 randomly selected students are 67, 74, 70, 70, 65, 62, 60, and 68.

**Tasks:**

1. Calculate the sample mean (represented by \( \bar{x} \)).

   - \( \bar{x} = 12.34 \) (Note: This value is a placeholder and should be calculated based on the given heights.)

2. Determine the margin of error at a 99% confidence level.

   - Margin of error: \( \pm 1.23 \) (Note: This value is also a placeholder and should be computed using the appropriate statistical methods.)

3. Calculate the 99% confidence interval for the mean height.

   - 99% confidence interval: \([ \bar{x} - 1.23, \bar{x} + 1.23 ]\)

**Instructions:**

- Insert your calculated values to determine the confidence interval.
- Enter values as the smaller number first, followed by the larger value.

**Interaction:**

- Enter your calculations and check your answers using the input box.
- Click "Check" to validate your calculated confidence interval.
- Use the "Next" button to proceed to the following step after a correct input. 

**Feedback:**

- Provide feedback on this section if necessary.

**Task Summary:**

- This exercise is part of Week 4: Readings and Assignments, with a due date of March 31, 2021, at 7:59 PM.
Transcribed Image Text:### Confidence Intervals for Population Means #### Challenge Activity: 5.7.1 Confidence Intervals for Population Means **Scenario:** Suppose the mean height in inches of all 9th-grade students at one high school is estimated. The population standard deviation is 3 inches. The heights of 8 randomly selected students are 67, 74, 70, 70, 65, 62, 60, and 68. **Tasks:** 1. Calculate the sample mean (represented by \( \bar{x} \)). - \( \bar{x} = 12.34 \) (Note: This value is a placeholder and should be calculated based on the given heights.) 2. Determine the margin of error at a 99% confidence level. - Margin of error: \( \pm 1.23 \) (Note: This value is also a placeholder and should be computed using the appropriate statistical methods.) 3. Calculate the 99% confidence interval for the mean height. - 99% confidence interval: \([ \bar{x} - 1.23, \bar{x} + 1.23 ]\) **Instructions:** - Insert your calculated values to determine the confidence interval. - Enter values as the smaller number first, followed by the larger value. **Interaction:** - Enter your calculations and check your answers using the input box. - Click "Check" to validate your calculated confidence interval. - Use the "Next" button to proceed to the following step after a correct input. **Feedback:** - Provide feedback on this section if necessary. **Task Summary:** - This exercise is part of Week 4: Readings and Assignments, with a due date of March 31, 2021, at 7:59 PM.
Expert Solution
Step 1

The population standard deviation(s) for 9th grade students is 3 inches.

The students have heights -67,74,70,70,65,62,60 and 68.

We need to find the mean. mean is the average value of the observations that is obtained by adding all the values and dividing it with the total no. of observations.

Mean(X)=1ni=1nXi

Margin of error is the amount of random sampling error in the results of a survey.

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