learn-co-curriculum / dsc-quiz-central-limit-confidence-intervals

Central Limit Theorem and Confidence Intervals

While we recommend using Python to find the answers to these questions, it is not required. You are more than welcome to use a calculator or pencil and paper to solve them, too.

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Sampling Distributions, Central Limit Theorem, Confidence Intervals

?: Question 1

What is a sampling distribution?

( ) The distribution of data points within a single sample from a population.

(X) The probability distribution that shows every possible result a statistic can take.

( ) A distribution with mean 0 and standard deviation 1.

?: Question 2

What is the correct way to interpret a 95% confidence interval for the population mean?

( ) A 95% confidence interval is the interval that contains 95% of values in a sample.

(X) If we pull many samples and construct different confidence intervals for the population mean, we expect 95% of the intervals to contain the true population mean.

( ) There is a 95% probability that the population mean lies between the lower and upper bounds of the 95% confidence interval.

( ) A 95% confidence interval implies that 95% of all possible sample means fall within the range of the interval.

?: Question 3

What factors affect the size of the confidence interval for a population mean? Select all applicable answers. For the purposes of the question, you may assume you do not know the population standard deviation.

[X] Sample size

[X] Sample standard deviation

[ ] Sample mean

[X] Confidence level

?: Question 4

How do you obtain the critical value for the test statistic in the case you want to determine the 95% confidence interval for the mean and you don't know the population standard deviation? Assume your sample size is equal to n = 25.

( ) stats.t.ppf(q=0.95, df=24)

(X) stats.t.ppf(q=0.975, df=24)

( ) stats.norm.ppf(q=0.95)

( ) stats.norm.ppf(q=0.975, df=24)

( ) stats.norm.ppf(q=0.975)

?: Question 5

Select all true statements from the choices below:

[X] Sampling error decreases as the sample size increases.

[ ] Estimates of population parameters are known as statistics.

[X] By the central limit theorem, the sampling distribution of a population parameter is normally distributed.

[ ] Higher confidence levels result in narrower confidence intervals.

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