For a new advertising campaign, a video game retailer is interested in including information on the average play time of their most popular game. They get 100 random samples of 40 players and obtain their play time to get a sampling distribution. The mean of the sampling distribution is 26.7 hours. In this example, what is the value of ?
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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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
If and , find the probability of getting a sample mean above 3.5 in a sample of 60 people.
A
0.009
B
0.018
C
0.003
D
0.006

1
Step 1: Identify the given values in the problem. The population mean (μ_X) is 3.2, the population standard deviation (σ_X) is 0.98, and the sample size (n) is 60. We are tasked with finding the probability of the sample mean being greater than 3.5.
Step 2: Calculate the standard error of the mean (SE). The formula for the standard error is SE = σ_X / sqrt(n). Substitute the given values into the formula: SE = 0.98 / sqrt(60).
Step 3: Standardize the sample mean to find the z-score. The formula for the z-score is z = (X̄ - μ_X) / SE, where X̄ is the sample mean. Substitute the values: z = (3.5 - 3.2) / SE.
Step 4: Use the z-score to find the probability. Look up the z-score in the standard normal distribution table or use statistical software to find the area to the right of the z-score, which represents the probability of the sample mean being greater than 3.5.
Step 5: Interpret the result. The probability obtained from the z-score calculation corresponds to the likelihood of observing a sample mean above 3.5 given the population parameters and sample size.
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