The Following Histogram Shows the Distribution of 1000 Sample Observations

question 29

Multiple Choice

The following histogram shows the distribution of 1000 sample observations from a population with a mean of  = 4 and a variance of ² = 8. Suppose a simple random sample of 100 observations is to be selected from the population and the sample average is calculated.Which of the following statements about the distribution of is/are FALSE?

• A)The distribution of will have a mean of 4.
• B)The distribution will be approximately Normal.
• C)Because the distribution shown in the histogram above is clearly skewed to the right,the shape of the distribution of will also show skewness to the right.
• D)Even though the distribution of the population variable appears to be skewed to the right,the distribution of will be approximately symmetric around  = 4.
• E)The standard deviation of the distribution of will be 0.283.

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Definitions:

Confidence

The measure of certainty or belief in the effectiveness, quality, or reliability of something, often used in statistical analysis or personal assurance.

Sample Proportion

The fraction or percentage of observations from a particular category within a sample, used in statistics to make inferences about populations.

Sample Size

The number of observations or replicates included in a statistical sample.

Allowance Factor

A coefficient or multiplier that accounts for expected deviations from standard or nominal conditions, often used in design and engineering to ensure safety or compliance.