Question 1

Which of the following statements best describes what a 95% confidence interval for a population mean actually tells us?

Accepted Answer

If we repeated the sampling process many times, about 95% of the calculated intervals would contain the true population mean.

Question 2

A researcher wants to estimate the proportion of defective products in a factory. She samples 200 products and finds 30 are defective. What is the 95% confidence interval for the proportion of defective products? (Use $$z^* = 1.96)$$

Accepted Answer

$$ (0.105, 0.195) $$

Question 3

Which of the following factors does NOT affect the margin of error in a confidence interval for the mean?

Accepted Answer

Sample mean

Question 4

A hospital claims their new treatment reduces average recovery time to less than 30 days. You sample 25 patients and find a mean recovery time of 28 days with a standard deviation of 6 days. What is the correct set of hypotheses for a left-tailed test?

Accepted Answer

$$ H_0$: \mu = 30 \quad vs \quad H_1$: \mu \u003c 30 $$

Question 5

If you want to construct a 99% confidence interval for a mean with a margin of error no greater than 10, and the population standard deviation is 25, what is the minimum sample size required?

Accepted Answer

42

Question 6

A company claims at least 85% of their clients are satisfied. In a sample of 100 clients, 78 are satisfied. At $$\alpha = 0.1$$, what is the correct conclusion?

Accepted Answer

There is enough evidence to reject the claim; satisfaction is less than 85%.

Question 7

Which of the following is an assumption required to use the Student’s T-distribution for inference about the mean?

Accepted Answer

The data comes from a normal distribution.

Question 8

As the degrees of freedom increase, what happens to the critical values of the Student’s T-distribution?

Accepted Answer

They get smaller and approach the critical Z values.

Question 9

You are running a hypothesis test for a population proportion. Which of the following must be true to use the Z-test?

Accepted Answer

$$ np \geq 5 $$ and $$ nq \geq 5 $$

Question 10

A regression model is given by $$ y = 3.52x - 12 . $$What is the predicted value of $$ y $$ when $$ x = 15 $$?

Accepted Answer

40.8

Question 11

Which of the following best describes extrapolation in the context of regression analysis?

Accepted Answer

Predicting $$ y $$ for $$ x $$ values outside the range of observed $$ x $$ values.

Question 12

Which of the following is the correct alternative hypothesis if you want to test whether the mean weight of cinnamon rolls is greater than 7 ounces?

Accepted Answer

$$ H_1$: \mu \u003e 7 $$

Question 13

A correlation coefficient $$ r = -0.91 $$ between two variables indicates:

Accepted Answer

A strong negative linear relationship

Question 14

Which of the following is NOT an appropriate conclusion from a hypothesis test?

Accepted Answer

Accept the null hypothesis

Question 15

Given a sample size of 18, what is the critical t-value for a 90% confidence interval?

Accepted Answer

1.740

Question 16

A company claims their mixed nuts contain no more than 50% peanuts. You believe there is more than 50% peanuts. What is the correct alternative hypothesis?

Accepted Answer

$$ H_1$: p \u003e 0.5 $$

Question 17

Which of the following is NOT an assumption required to run a One-Way ANOVA test?

Accepted Answer

Each sample must be categorical.

Question 18

If the correlation between two variables is positive, what does this mean?

Accepted Answer

As one variable increases, the other variable also increases.

Question 19

You are using a regression model to predict the height of elementary school children based on age. For which of the following is it appropriate to use this model?

Accepted Answer

Predicting the height of a 2nd grader

Question 20

What is the main indicator for whether to use the Z or T distribution when running a hypothesis test for the mean?

Accepted Answer

Whether the population standard deviation is known

Comprehensive Step-by-Step Guidance for College Statistics Final Exam Study Guide

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