Q: A study finds that the mean cholesterol level in a sample of 36 patients is 200 mg/dL with a standard deviation of 18 mg/dL. What is the 95% confidence interval for the mean cholesterol level? (Use $$z^* = 1.96)$$

$$200 \pm 1.96 \times \dfrac{18}{6}$$

Question 1

A pharmaceutical company wants to estimate the average recovery time for a new drug. They randomly select 100 patients from a hospital and record their recovery times. Which type of sampling method is being used?

Accepted Answer

Simple random sampling

Question 2

Which of the following best describes the difference between a population and a sample?

Accepted Answer

A population includes all members of a group, while a sample is a subset.

Question 3

A researcher records the number of cars passing through an intersection every hour for a week. Which type of data is being collected?

Accepted Answer

Discrete quantitative data

Question 4

Which of the following is the correct formula for the probability of the union of two mutually exclusive events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$

Question 5

A fair six-sided die is rolled twice. What is the probability that both rolls result in a 3?

Accepted Answer

$$\dfrac{1}{36}$$

Question 6

Which of the following statements about the standard normal distribution is TRUE?

Accepted Answer

It has a mean of 0 and a standard deviation of 1.

Question 7

A company claims that 60% of its products pass quality control. If 10 products are selected at random, what is the probability that exactly 7 pass? (Use the binomial probability formula.)

Accepted Answer

$$\binom{10}{7} (0.6)^7$ (0.4)^3$

Question 8

Which of the following is NOT a requirement for a probability distribution to be considered binomial?

Accepted Answer

The trials are dependent on each other.

Question 9

A histogram is best used for which type of data?

Accepted Answer

Continuous quantitative data

Question 10

If the mean of a data set is 50 and the standard deviation is 5, what is the z-score for a value of 60?

Accepted Answer

$$z = 2$$

Question 11

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 12

A researcher wants to test if a new teaching method is more effective than the traditional method. Which hypothesis test should be used if the researcher compares the mean scores of two independent groups?

Accepted Answer

Two-sample t-test

Question 13

Which of the following is the correct formula for the confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

$$\bar{x} \pm z^* \dfrac{\sigma}{\sqrt{n}}$$

Question 14

A hospital administrator wants to know if the proportion of patients recovering within 3 days has changed from last year’s rate of 0.4. Which statistical test should be used?

Accepted Answer

One-sample z-test for proportions

Question 15

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient of -1 indicates a perfect negative linear relationship.

Question 16

A study finds that the mean cholesterol level in a sample of 36 patients is 200 mg/dL with a standard deviation of 18 mg/dL. What is the 95% confidence interval for the mean cholesterol level? (Use $$z^* = 1.96)$$

Accepted Answer

$$200 \pm 1.96 	imes \dfrac{18}{6}$$

Question 17

Which of the following is an example of a Type I error?

Accepted Answer

Rejecting a true null hypothesis

Question 18

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 19

A scatterplot shows a strong, positive linear relationship between two variables. Which of the following is most likely true?

Accepted Answer

The correlation coefficient is close to 1.

Question 20

A researcher is testing whether the mean weight of a certain species of fish is different in two lakes. The samples are independent. Which test should be used?

Accepted Answer

Two-sample t-test

Statistics Study Guide: Probability, Distributions, and Statistical Inference

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