Question 1

Which of the following best describes the difference between a probability distribution and a sampling distribution?

Accepted Answer

A probability distribution describes the possible values of a random variable from the population, while a sampling distribution describes the possible values of a statistic (such as the mean) computed from samples.

Question 2

Suppose you have a box containing marbles labeled 1, 2, 3, and 4. If you randomly select one marble, what is the mean ($$\mu) of $$the marble labels?

Accepted Answer

$$\mu = \dfrac{1+2+3+4}{4} = 2.5$$

Question 3

If you draw two marbles from the box (with replacement), what is the variance of the sampling distribution of the sample mean $$\overline{X}$$?

Accepted Answer

$$\$$sigma^2$$_{\overline{X}} = \dfrac{1.25}{2} = 0.625$$

Question 4

Which statement about the Central Limit Theorem (CLT) is correct?

Accepted Answer

The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 5

A researcher wants to estimate the mean blood pressure of adult males. The population standard deviation is known to be $$\sigma = 12$$ mmHg. What is the standard error (SE) of the mean for a sample size of $$n = 36$$?

Accepted Answer

$$SE = \dfrac{12}{\sqrt{36}} = 2$$

Question 6

When should you use the t-distribution instead of the z-distribution for constructing a confidence interval for the mean?

Accepted Answer

When the sample size is small ($$n \u003c 30) $$and the population standard deviation is unknown.

Question 7

A sample of 16 healthy adults has a mean arterial blood gas pH of 85 mmHg and a sample standard deviation of 7 mmHg. What is the standard error (SE) of the mean?

Accepted Answer

$$SE = \dfrac{7}{\sqrt{16}} = 1.75$$

Question 8

Which of the following will result in a narrower (more precise) confidence interval for the mean?

Accepted Answer

Increasing the sample size $$n$$

Question 9

A community survey finds that 39 out of 90 randomly selected individuals believe in 'albularyo.' What is the point estimate for the proportion $$p$$?

Accepted Answer

$$p = \dfrac{39}{90} = 0.433$$

Question 10

In a study comparing passing rates, 80 out of 95 females and 45 out of 55 males passed Math 101. What is the point estimate for the difference in proportions ($$p_1$$ - $$p_2$$)?

Accepted Answer

$$p_1$$ - $$p_2$$ = \dfrac{80}{95} - \dfrac{45}{55} = 0.842 - 0.818 = 0.024$$

Question 11

A researcher wants to estimate the mean serum creatinine level in patients after receiving a new antibiotic. If $$s = 0.4 mg/dL $$and $$n = 12$$, what is the standard error (SE)?

Accepted Answer

$$SE = \dfrac{0.4}{\sqrt{12}} = 0.115$$

Question 12

Which formula is used to determine the required sample size $$n$$ for estimating a population proportion $$p$$ with a specified margin of error $$E$$ and confidence level (z-critical value $$z$$)?

Accepted Answer

$$n = \dfrac{z^2$ p (1-p)}{E^2$}$$

Question 13

A health researcher wants to estimate the difference in mean systolic blood pressure between smokers and non-smokers with a margin of error of 5 mmHg and 95% confidence. The estimated standard deviations are 12 and 10 mmHg, respectively. What is the formula for the required sample size per group?

Accepted Answer

$$n = \dfrac{z^2$ (\$$sigma_1$$^2 + \$$sigma_2$$^2)}{E^2$}$$

Question 14

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A 95% confidence interval means that if we repeat the sampling many times, about 95% of the intervals will contain the true population parameter.

Question 15

If the sample size $$n$$ increases, what happens to the standard error (SE) of the mean?

Accepted Answer

SE decreases because $$SE = \dfrac{\sigma}{\sqrt{n}}$$

Question 16

A sample of 32 patients has a mean serum creatinine level of 1.2 mg/dL and $$s = 0.4 mg/dL. $$What is the 95% confidence interval for the mean? (Use $$z = 1.96)$$

Accepted Answer

$$(1.06, 1.34)$$

Question 17

Which of the following is a correct formula for the margin of error (ME) in a confidence interval for the mean?

Accepted Answer

$$ME = (CV) 	imes (SE)$$

Question 18

In a paired sample experiment, the mean difference $$\overline{d} is 5.3 $$and the standard deviation of the differences $$s_d is 3.302 $$for $$n = 10$$ pairs. What is the standard error of the mean difference?

Accepted Answer

$$SE = \dfrac{3.302}{\sqrt{10}} = 1.044$$

Module 8

Study Guide - Practice Questions

Study Guide - Flashcards