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

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

Question 1

A researcher wants to compare the average battery life of two brands of smartphones. Which of the following best describes the type of statistical method the researcher should use?

Accepted Answer

Inferential statistics, because the researcher wants to make conclusions about the population based on sample data.

Question 2

Which of the following variables is best classified as discrete and quantitative?

Accepted Answer

The number of defective products in a batch.

Question 3

A company wants to estimate the proportion of defective items produced in a day. They take a random sample of 200 items and find 12 are defective. What is the point estimate for the population proportion of defective items?

Accepted Answer

$$ \frac{12}{200} = 0.06 $$

Question 4

Which of the following statements about the mean and median is TRUE for a data set that is highly skewed to the right?

Accepted Answer

The mean is greater than the median.

Question 5

A hospital administrator wants to visualize the distribution of patient wait times (a continuous variable) in the emergency room. Which graphical method is most appropriate?

Accepted Answer

Histogram

Question 6

Given the following five-number summary for the ages of patients at a clinic: $$ 	ext{Min} = 18 $$, $$ Q_1$ = 25 $$, $$ 	ext{Median} = 32 $$, $$ Q_3$ = 45 $$, $$ 	ext{Max} = 80 . $$What is the interquartile range (IQR)?

Accepted Answer

$$ 45 - 25 = 20 $$

Question 7

A pharmaceutical company claims that their new drug increases the average lifespan of patients by more than 2 years. Which of the following is the correct null hypothesis ($$ H_0$ ) $$for testing this claim?

Accepted Answer

$$ H_0$: \mu \leq 2 $$

Question 8

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$ \frac{2}{6} = \frac{1}{3} $$

Question 9

Which of the following best describes the difference between correlation and causation?

Accepted Answer

Causation implies correlation, but correlation does not imply causation.

Question 10

A sample of 100 light bulbs has a mean lifetime of 1200 hours and a standard deviation of 100 hours. Using the Empirical Rule, approximately what percentage of bulbs are expected to have lifetimes between 1100 and 1300 hours?

Accepted Answer

About 68%

Question 11

A student scores 85 on a test with a class mean of 75 and a standard deviation of 5. What is the student's z-score?

Accepted Answer

$$ z = \frac{85 - 75}{5} = 2 $$

Question 12

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is always skewed to the right.

Question 13

A quality control manager inspects 10 items from a production line and records the number of defective items. Which probability distribution is most appropriate for modeling the number of defectives?

Accepted Answer

Binomial distribution

Question 14

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 15

A sample of 36 students has a mean test score of 80. The population standard deviation is known to be 12. What is the standard error of the mean?

Accepted Answer

$$ \frac{12}{\sqrt{36}} = 2 $$

Question 16

A 95% confidence interval for a population mean is calculated as (50, 60). Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 17

A researcher is testing $$ H_0$: p = 0.5 $$ against $$ H_a: p 
eq 0.5  at$$ $$ \alpha = 0.05 . If $$the p-value is 0.03, what is the correct conclusion?

Accepted Answer

Reject $$ H_0$ $$ because 0.03 \u003c 0.05.

Question 18

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

Accepted Answer

Rejecting a true null hypothesis.

Question 19

A scatter diagram shows a strong positive linear relationship between hours studied and exam scores. Which of the following is the most appropriate interpretation?

Accepted Answer

As hours studied increase, exam scores tend to increase.

Question 20

A sample of 25 patients has a mean cholesterol level of 200 mg/dL. The sample standard deviation is 20 mg/dL. What is the 95% confidence interval for the mean cholesterol level? (Use $$ t_{0.025, 24} = 2.064 )$$

Accepted Answer

$$ 200 \pm 2.064 	imes \frac{20}{\sqrt{25}} = 200 \pm 8.256 $$

STA 2023: Statistical Methods – Syllabus and Study Guide Overview

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