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 flips a coin 100 times and observes 65 heads. What is the 90% confidence interval for the proportion of heads observed? (Use $$z^* = 1.645$$ for 90% confidence.)

Accepted Answer

$$ (0.572, 0.728) $$

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 cereal company claims their bags contain an average of 80 ounces of cereal with a standard deviation of 7 ounces. A sample of 36 bags has a mean of 77 ounces. What is the 95% confidence interval for the mean weight? (Use $$z^* = 1.96.)$$

Accepted Answer

$$ (74.71, 79.29) $$

Question 5

If you want a 95% confidence interval for the mean to have a margin of error of 5, and the population standard deviation is 10, what is the minimum sample size required?

Accepted Answer

$$ n = 16 $$

Question 6

Which of the following is the correct set of hypotheses for a right-tailed hypothesis test for the mean?

Accepted Answer

$$ H_0$: \mu = \mu_0$ \quad vs \quad H_1$: \mu \u003e \mu_0$ $$

Question 7

A company claims at least 85% of their clients are satisfied. In a sample of 100 clients, 78 are satisfied. At $$\alpha = 0.1$$, do you have enough evidence to reject the company's claim?

Accepted Answer

Yes, because the p-value is less than 0.1

Question 8

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

Accepted Answer

The population standard deviation is unknown

Question 9

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

Accepted Answer

They decrease and approach the critical Z values

Question 10

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

Accepted Answer

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

Question 11

A regression model is given by $$ y = 3.52x - 12 . $$What is the predicted value of $$ y $$ when $$ x = 10 $$?

Accepted Answer

$$ 23.2 $$

Question 12

Which of the following best describes interpolation in the context of regression models?

Accepted Answer

Predicting $$ y $$ for $$ x $$ values within the range of observed $$ x $$ values

Question 13

Which of the following is the correct alternative hypothesis if you want to test whether Cinnabon cinnamon rolls are larger than the claimed 7 ounces?

Accepted Answer

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

Question 14

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

Accepted Answer

A strong, negative linear relationship

Question 15

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

Accepted Answer

Accept the null hypothesis

Question 16

Given the regression model $$ y = 0.813x + 0.14 $$, where $$ x  is $$the weight of a child in kg, what is the predicted metabolic rate (in 100 kcal/day) for a child weighing 20 kg?

Accepted Answer

$$ 16.4 $$

Question 17

Which of the following is the correct null and alternative hypothesis for a One-Way ANOVA test?

Accepted Answer

$$ H_0$: $$ All means are equal $$ \quad vs \quad H_1$:  At $$least one mean is different

Question 18

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

Accepted Answer

Each sample must have a different variance

Question 19

If the correlation between two variables is negative, what does this mean about their relationship?

Accepted Answer

As one variable increases, the other decreases

Question 20

Which of the following 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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