Constructing a Confidence Interval In Exercises 25–28, use the da...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

3. Describing Data Numerically

Mean

Statistics

3. Describing Data Numerically

Mean

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1:40 minutes

Problem 6.2.28a

Textbook Question

Constructing a Confidence Interval In Exercises 25–28, use the data set to (a) find the sample mean. Assume the population is normally distributed.
Homework The weekly time spent (in hours) on homework for 18 randomly selected high school students

Verified step by step guidance

Step 1: Identify the data set provided. The weekly time spent on homework (in hours) for 18 students is given as: 12.0, 11.3, 13.5, 11.7, 12.0, 13.0, 15.5, 10.8, 12.5, 12.3, 14.0, 9.5, 8.8, 10.0, 12.8, 15.0, 11.8, 13.0.

Step 2: Calculate the sample mean. To find the sample mean, sum all the values in the data set and divide by the total number of observations (n = 18). Use the formula:

μ = \frac{\sum x}{n}

, where ∑x is the sum of all data points and n is the sample size.

Step 3: Add all the values in the data set. Perform the summation:

\sum x = 12.0 + 11.3 + 13.5 + 11.7 + 12.0 + 13.0 + 15.5 + 10.8 + 12.5 + 12.3 + 14.0 + 9.5 + 8.8 + 10.0 + 12.8 + 15.0 + 11.8 + 13.0

Step 4: Divide the sum obtained in Step 3 by the sample size (n = 18). Use the formula:

μ = \frac{\sum x}{18}

Step 5: Interpret the sample mean. The sample mean represents the average weekly time spent on homework by the 18 students in the sample. This value will be used in further calculations, such as constructing a confidence interval.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sample Mean

The sample mean is the average of a set of values, calculated by summing all the observations and dividing by the number of observations. In this context, it represents the average time spent on homework by the selected high school students. It is a key statistic used to estimate the population mean when the entire population cannot be measured.

Confidence Interval

A confidence interval is a range of values, derived from a sample, that is likely to contain the population parameter (like the population mean) with a specified level of confidence, typically 95% or 99%. It provides an estimate of uncertainty around the sample mean, indicating how much the sample mean might vary from the true population mean.

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In this question, assuming the population is normally distributed allows for the use of specific statistical methods to calculate the confidence interval, as many statistical techniques rely on this assumption for validity.

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Constructing a Confidence Interval In Exercises 25–28, use the data set to (a) find the sample mean. Assume the population is normally distributed.Homework The weekly time spent (in hours) on homework for 18 randomly selected high school students