Question 1

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

Accepted Answer

A population includes all members of a defined group, while a sample is a subset of that group selected for analysis.

Question 2

A researcher wants to compare the average test scores of two different teaching methods. Which statistical test is most appropriate for this scenario?

Accepted Answer

A two-sample t-test for means

Question 3

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$$

Question 4

A pharmaceutical company wants to test if a new drug is more effective than the current standard. Which of the following best describes the null hypothesis $$H_0$$ for this test?

Accepted Answer

$$H_0$$: The new drug is equally effective as the current standard.

Question 5

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

Accepted Answer

The mean, median, and mode are all equal in a normal distribution.

Question 6

Suppose you roll a fair six-sided die 60 times. What is the expected number of times you will roll a '4'?

Accepted Answer

10

Question 7

Which of the following is the correct formula for the standard deviation $$s of a $$sample of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

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

Question 8

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 9

Which of the following is an example of a categorical variable?

Accepted Answer

Type of smartphone (iPhone, Android, Other)

Question 10

A researcher wants to test if the proportion of left-handed students in a university is different from 10%. Which test should be used?

Accepted Answer

One-sample z-test for proportions

Question 11

Which of the following best describes the purpose of a confidence interval?

Accepted Answer

To estimate a population parameter with an associated level of confidence

Question 12

If a data set is skewed to the right, which of the following is most likely TRUE?

Accepted Answer

The mean is greater than the median.

Question 13

Which of the following is the correct formula for the probability of exactly $$k$$ successes in $$n$$ independent Bernoulli trials with probability $$p of $$success?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 14

A hospital administrator wants to know if there is an association between gender (male/female) and preference for a new hospital service (yes/no). Which statistical test should be used?

Accepted Answer

Chi-square test for independence

Question 15

Which of the following is a key assumption for using the two-sample t-test for means?

Accepted Answer

The two samples are independent and come from populations with equal variances.

Question 16

A company claims that their batteries last an average of 100 hours. A consumer group tests 25 batteries and finds a sample mean of 98 hours with a standard deviation of 5 hours. What is the value of the test statistic for a one-sample t-test?

Accepted Answer

$$t = \frac{98 - 100}{5/\sqrt{25}} = -2.0$$

Question 17

Which of the following best describes the purpose of a goodness-of-fit test?

Accepted Answer

To determine if observed categorical data fit a specified distribution

Question 18

A linear regression analysis yields the equation $$y = 2x + 5. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$y = 2(4) + 5 = 13$$

Question 19

Which of the following is NOT a reason to use random sampling in a statistical study?

Accepted Answer

To guarantee that the sample mean equals the population mean

Question 20

Which of the following is the correct formula for the correlation coefficient $$r$$ between two variables $$x$$ and $$y$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Introduction to Statistics – Syllabus and Study Guide

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