A psychologist surveys 6060 people about the number of close friends they have. The mean is 4.34.3, with a standard deviation of 2.82.8. The distribution is strongly skewed right. Why is a large sample size necessary when constructing a confidence interval for the mean number of close friends?

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1. Intro to Stats and Collecting Data(0)

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Visualizing Qualitative vs. Quantitative Data
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Frequency Distributions
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Time-Series Graph
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3. Describing Data Numerically(0)

Mean
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Median
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Counting
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Uniform Distribution
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Non-Standard Normal Distribution
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7. Sampling Distributions & Confidence Intervals: Mean(0)

Sampling Distribution of the Sample Mean and Central Limit Theorem
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Introduction to Confidence Intervals
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Confidence Intervals for Population Mean
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Determining the Minimum Sample Size Required
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Sampling Distribution of Sample Proportion
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Chi Square Distribution
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7. Sampling Distributions & Confidence Intervals: Mean

Sampling Distribution of the Sample Mean and Central Limit Theorem

7. Sampling Distributions & Confidence Intervals: Mean

Sampling Distribution of the Sample Mean and Central Limit Theorem: Videos & Practice Problems

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Problem 55Multiple Choice

A psychologist surveys $60$ people about the number of close friends they have. The mean is $4.3$ , with a standard deviation of $2.8$ . The distribution is strongly skewed right. Why is a large sample size necessary when constructing a confidence interval for the mean number of close friends?

Because a large sample size forces the data to be normally distributed

Because the central limit theorem allows the use of normal-based confidence intervals for the mean when the sample size is large, even if the data is skewed

Because a large sample size makes the mean equal to the median

Because a large sample size removes all variability from the data

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