Sampling Distributions and the Central Limit Theorem: The National Survey of Student Engagement asks college students...

Sampling Distributions and the Central Limit Theorem:

The National Survey of Student Engagement asks college students questions about the quality of their education. In 2018, NSSE reported the following result about college freshman:

During the current school year, about how often have you used numerical information to examine a real-world problem or issue (unemployment, climate change, public health, etc.)?

Mean: 2.29 SD: .92

These results were based on a survey of over 500,000 students from 725 institutions. Suppose we want to see how Coker College students compare to the national results by taking independent, random samples of 35 students each. Find the mean μ_x ̅ and standard deviation σ_x ̅ of this sampling distribution. (Hint: Use the Central Limit Theorem)

Find the probability that the sample mean of a random sample of 35 Coker College students for number of times using numerical information to examine real world issues is more than 3.

In this class, we've used numerical data to examine crime, genetic traits of fungus, political polling, and many other real-world topics. Would it be appropriate to say our statistics class sample of 19 students is unusual compared to the national average? Why or why not?

Expert Solution

Find the mean μ_x ̅ and standard deviation σ_x ̅ of this sampling distribution. (Hint: Use the Central Limit Theorem)

According to central limit theorem,
If the sample size is more than 30, then
sample mean is equal to mean of the population
sample standard deviation is equal to

Find the probability that the sample mean of a random sample of 35 Coker College students for number of times using numerical information to examine real world issues is more than 3.

In this class, we've used numerical data to examine crime, genetic traits of fungus, political polling, and many other real-world topics. Would it be appropriate to say our statistics class sample of 19 students is unusual compared to the national average? Why or why not?

It is unusual to compare it since the sample size is very small compared to the population. Also the sample size should be greater than 30 to apply the central limit theorem.

orchestra answered 1 year ago

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