Question 1

What does the diagram illustrate about the relationship between a population and a sample in statistics?

Accepted Answer

It shows that a sample is used to make inferences about the population.

Question 2

Which of the following best describes statistical inference as depicted in the diagram?

Accepted Answer

Drawing conclusions about a population based on information from a sample.

Question 3

According to the study materials, which of the following is NOT a method of making statistical inference?

Accepted Answer

Regression analysis for two populations.

Question 4

What is a sampling distribution?

Accepted Answer

A probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population.

Question 5

Which formula is used to standardize the sample mean to a standard normal distribution?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$

Question 6

If the time spent in the shower is normally distributed with $$\mu = 12.5$$ minutes and $$\sigma = 3.5$$ minutes, what is the probability that the mean time for a sample of 25 people is less than 14 minutes?

Accepted Answer

0.9838

Question 7

According to the Central Limit Theorem, what happens to the sampling distribution of the sample mean as the sample size increases?

Accepted Answer

It approaches a normal distribution regardless of the population's distribution.

Question 8

What is the standard error of the mean for a population with $$\sigma = 3.5$$ and a sample size of $$n = 49$$?

Accepted Answer

$$0.5$$

Question 9

Which of the following is the correct formula for the standard deviation of the sampling distribution of sample proportions?

Accepted Answer

$$\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$$

Question 10

A researcher wants to estimate the average time students spend on homework. If the distribution is highly skewed, what should the researcher do to ensure the sampling distribution of the mean is approximately normal?

Accepted Answer

Increase the sample size to be much larger than 30.

Question 11

If $$n = 9$$, $$\mu = 12.5$$, $$\sigma = 3.5$$, what is the $$z-$$score for a sample mean of $$15.2$$ minutes?

Accepted Answer

$$z = \frac{15.2 - 12.5}{3.5 / \sqrt{9}} = 2.31$$

Question 12

Which of the following statements about sample proportions is TRUE?

Accepted Answer

As the sample size increases, the sampling distribution of the sample proportion becomes more normal.

Question 13

Why is the Central Limit Theorem important in inferential statistics?

Accepted Answer

It allows us to use the normal distribution to make inferences about the population mean, even if the population is not normal.

Question 14

A company wants to know the proportion of defective products. If $$p = 0.1$$ and $$n = 100$$, what is the standard deviation of the sampling distribution of the sample proportion?

Accepted Answer

$$\sqrt{\frac{0.1 	imes 0.9}{100}} = 0.03$$

Question 15

Which of the following is a point estimate in inferential statistics?

Accepted Answer

The sample mean $$\bar{x}.$$

Sampling Distributions and Statistical Inference: Study Notes

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