Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A researcher collects the heights of 100 randomly selected college students to estimate the average height of all college students in the country. In this context, which is the sample and which is the population?

Accepted Answer

The 100 students are the sample; all college students in the country are the population.

Question 3

Which of the following is an example of a nominal level of measurement?

Accepted Answer

Types of cuisine (Italian, Chinese, Mexican, Indian)

Question 4

Suppose you roll two fair six-sided dice. What is the probability that the sum is 7?

Accepted Answer

$$ \frac{6}{36} $$

Question 5

Which formula correctly calculates the sample variance $$ s^2$ $$ for a data set $$ x_1$, x_2$, ..., x_n $$?

Accepted Answer

$$ s^2$ = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$ $$

Question 6

A normal random variable $$ X $$ has mean $$ \mu = 50 $$ and standard deviation $$ \sigma = 10 . $$What is the $$ z -$$score for $$ X = 65 $$?

Accepted Answer

$$ z = 1.5 $$

Question 7

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 8

A 95% confidence interval for a population mean $$ \mu  is $$calculated as $$ (12.5, 17.5) . $$Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the true population mean $$ \mu $$ lies between 12.5 and 17.5.

Question 9

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

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 10

Suppose the correlation coefficient $$ r $$ between two variables is $$ -0.85 . $$Which of the following best describes their relationship?

Accepted Answer

There is a strong negative linear relationship.

Question 11

Given the regression line $$ \hat{y} = 2 + 3x $$, what is the predicted value of $$ y $$ when $$ x = 4 $$?

Accepted Answer

$$ 14 $$

Question 12

Which of the following best describes an observational study?

Accepted Answer

Researchers collect data without manipulating variables.

Question 13

If $$ P(A) = 0.4 $$, $$ P(B) = 0.5 $$, and $$ P(A \cap B) = 0.2 $$, what is $$ P(A \cup B) $$?

Accepted Answer

$$ 0.7 $$

Question 14

Which formula gives the standard error of the sample mean when the population standard deviation $$ \sigma  is $$known?

Accepted Answer

$$ \frac{\sigma}{\sqrt{n}} $$

Question 15

A company claims that their batteries last an average of 100 hours. A sample of 36 batteries has a mean of 98 hours and a standard deviation of 6 hours. Test the claim at the 5% significance level. What is the value of the test statistic?

Accepted Answer

$$ z = \frac{98 - 100}{6/\sqrt{36}} = -2 $$

Question 16

Which of the following is NOT a requirement for using the normal approximation to the binomial distribution?

Accepted Answer

The sample size $$ n $$ must be small.

Question 17

If the null hypothesis is $$ H_0$: \mu = 50 $$ and the alternative is $$ H_a: \mu \u003e 50 $$, which of the following describes the test?

Accepted Answer

A right-tailed test

Question 18

Which of the following best describes the meaning of the $$ p -$$value in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

Question 19

Suppose you want to estimate the mean weight of apples in an orchard. Which sampling method would best avoid bias?

Accepted Answer

Randomly selecting apples from all areas of the orchard.

Statistics Final Exam Study Guide: Key Concepts and Formulas

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