A company’s marketing team takes 50 samples of 10 recent clients to create a sampling distribution of sample means for the average amount spent per month on company products. Can the Central Limit Theorem be used to determine that the sampling distribution is normal?
Table of contents
- 1. Introduction to Statistics53m
- 2. Describing Data with Tables and Graphs2h 1m
- 3. Describing Data Numerically1h 48m
- 4. Probability2h 26m
- 5. Binomial Distribution & Discrete Random Variables2h 55m
- 6. Normal Distribution & Continuous Random Variables1h 48m
- 7. Sampling Distributions & Confidence Intervals: Mean2h 8m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 20m
- 9. Hypothesis Testing for One Sample2h 23m
- 10. Hypothesis Testing for Two Samples3h 25m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 30m
- 14. ANOVA1h 4m
7. Sampling Distributions & Confidence Intervals: Mean
Sampling Distribution of the Sample Mean and Central Limit Theorem
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A researcher takes 10 samples of 20 students each to get a sampling distribution of the average number of siblings students at a university have. According to the Central Limit Theorem, what can the researcher do make their sampling distribution get closer to normal?
A
Increase the number of samples
B
Increase the sample size
C
Decrease sample size
D
Decrease number of samples

1
Step 1: Understand the Central Limit Theorem (CLT). The CLT states that as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the population's original distribution.
Step 2: Identify the factors that influence the normality of the sampling distribution. These include the sample size and the number of samples taken.
Step 3: To make the sampling distribution closer to normal, the researcher can increase the sample size. Larger sample sizes reduce variability and make the sampling distribution more normal.
Step 4: Another way to improve the normality of the sampling distribution is to increase the number of samples. More samples provide a better representation of the population and improve the accuracy of the sampling distribution.
Step 5: Avoid decreasing the sample size or the number of samples, as these actions would reduce the reliability and normality of the sampling distribution.
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