Basic Statistics & Hypothesis Testing (2024)

Question 1

The mode of a dataset is defined as:

Answer 1

The most frequently occurring value

Question 2

Which measure of central tendency is most affected by extreme values?

Answer 2

Mean

Question 3

What does the range of a dataset represent?

Answer 3

The difference between the highest and lowest values

Question 4

Which of the following best describes standard deviation?

Answer 4

A measure of spread in the data

Question 5

In statistics, what does a histogram represent?

Answer 5

The frequency of data within intervals

Question 6

Which type of data is represented by categories?

Answer 6

Categorical

Question 7

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Answer 7

68%

Question 8

What is the primary purpose of a scatter plot?

Answer 8

To analyze the relationship between two variables

Question 9

Which type of variable represents data that can take on any value within a range, like height?

Answer 9

Continuous

Question 10

If the mean of a dataset is 10 and the median is 15, the data is likely (describe the shape of the curve):

Answer 10

Skewed to the right

Question 11

Which measure of spread is calculated as the difference between the highest and lowest values?

Answer 11

Range

Question 12

What is the term for a sample that accurately represents the population from which it was drawn?

Answer 12

Random sample

Question 13

What type of graph is best for displaying the frequency of categorical data?

Answer 13

Bar chart

Question 14

If two events cannot happen at the same time, they are called:

Answer 14

Mutually exclusive

Question 15

The median is defined as:

Answer 15

The middle value when data is ordered

Question 16

Which of the following data types is continuous?

Answer 16

Gender

Question 17

What does a box plot display about a dataset?

Answer 17

The quartiles and median

Question 18

What is an outlier in a dataset?

Answer 18

A value much higher or lower than the rest

Question 19

Which of the following is a measure of central tendency?

Answer 19

Mean

Question 20

What is the sum of probabilities for all possible outcomes in a probability distribution?

Answer 20

100%

Question 21

The interquartile range (IQR) is the range of values between:

Answer 21

The minimum and maximum

Question 22

What is a bar graph typically used to display?

Answer 22

Continuous data

Question 23

Which type of data has meaningful zero points and can be used in calculations?

Answer 23

Ratio

Question 24

The probability of a single event is defined as:

Answer 24

The ratio of the number of favorable outcomes to the total outcomes

Question 25

Which of the following best describes the null hypothesis? A) The hypothesis that there is a significant effect. B) The hypothesis that the results are due to chance. C) The hypothesis that there is no significant difference. D) The hypothesis that all sample means are equal.

Answer 25

The hypothesis that there is no significant difference.

Question 26

In a hypothesis test, if the p-value is less than the significance level (α), you should: A) Fail to reject the null hypothesis. B) Reject the null hypothesis. C) Increase the sample size. D) Change the significance level.

Answer 26

Reject the null hypothesis.

Question 27

A Type I error occurs when: A) The null hypothesis is rejected when it is true. B) The null hypothesis is not rejected when it is false. C) The alternative hypothesis is accepted when it is false. D) There is insufficient evidence to make a decision.

Answer 27

The null hypothesis is rejected when it is true.

Question 28

Which of the following tests is appropriate for comparing means of two independent samples? A) Paired t-test B) Independent t-test C) Chi-square test D) ANOVA

Answer 28

Independent t-test

Question 29

In hypothesis testing, the p-value represents: A) The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. B) The probability that the null hypothesis is true. C) The probability that the alternative hypothesis is true. D) The probability of making a Type II error.

Answer 29

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

Question 30

When performing a hypothesis test for a population proportion, which distribution is generally used? A) Normal distribution B) Chi-square distribution C) t-distribution D) Exponential distribution

Answer 30

Normal distribution

Question 31

The level of significance in hypothesis testing is typically denoted by: A) β B) α C) p D) μ

Answer 31

α

Question 32

A p-value of 0.03 means: A) There is a 3% chance that the null hypothesis is true. B) There is a 3% chance that the results are due to random variation. C) There is a 97% chance that the null hypothesis is true. D) The probability of observing the sample results, given that the null hypothesis is true, is 3%.

Answer 32

The probability of observing the sample results, given that the null hypothesis is true, is 3%.

Question 33

In an ANOVA test, the null hypothesis is: A) The variances of the populations are equal. B) The population means are equal. C) The sample means are different. D) The population variances are different.

Answer 33

The population means are equal.

Question 34

What does a chi-square test measure? A) The mean difference between groups. B) The association between categorical variables. C) The probability of a continuous variable. D) The difference between paired sample means.

Answer 34

The association between categorical variables.

Question 35

The power of a test is defined as: A) The probability of rejecting the null hypothesis. B) The probability of accepting the null hypothesis. C) The probability of correctly rejecting a false null hypothesis. D) The probability of making a Type I error.

Answer 35

The probability of correctly rejecting a false null hypothesis.

Question 36

A Type II error occurs when: A) The null hypothesis is rejected when it is true. B) The null hypothesis is not rejected when it is false. C) The alternative hypothesis is rejected when it is false. D) There is insufficient evidence to make a decision.

Answer 36

The null hypothesis is rejected when it is true.

Question 37

Which of the following would increase the power of a test? A) Increasing sample size B) Increasing significance level C) Reducing variance D) All of the above

Answer 37

All of the above

Question 38

When should you use a paired t-test? A) Comparing two related groups B) Comparing two independent groups C) Comparing frequencies D) Comparing variances

Answer 38

Comparing two related groups

Question 39

The F-distribution is used in which of the following tests? A) Chi-square test B) t-test C) ANOVA D) Z-test

Answer 39

ANOVA

Question 40

What is the critical value in hypothesis testing? A) The probability of making a Type I error B) The threshold to reject the null hypothesis C) The value that must exceed the test statistic D) The effect size needed to reject the null hypothesis

Answer 40

The threshold to reject the null hypothesis

Question 41

The null hypothesis is rejected when: A) The p-value is greater than α B) The test statistic is within the confidence interval C) The p-value is less than α D) The sample mean is equal to the population mean

Answer 41

The p-value is less than α

Question 42

Which of the following would decrease the likelihood of a Type I error? A) Increasing sample size B) Decreasing α C) Increasing variance D) Using a two-tailed test

Answer 42

Decreasing α

Question 43

What is the alternative hypothesis in a hypothesis test? A) The hypothesis that predicts a difference B) The hypothesis that predicts no difference C) The hypothesis that the sample is biased D) The hypothesis that the population mean is zero

Answer 43

The hypothesis that predicts a difference

Question 44

The Central Limit Theorem states that: A) All sample distributions become normal B) The distribution of sample means will be approximately normal, regardless of the population distribution, as sample size increases C) The sample mean equals the population mean D) Variance decreases with larger samples

Answer 44

The distribution of sample means will be approximately normal, regardless of the population distribution, as sample size increases

Question 45

In a hypothesis test, the test statistic measures: A) The likelihood of a Type I error B) The effect size C) The amount of evidence against the null hypothesis D) The variability of the sample

Answer 45

The amount of evidence against the null hypothesis

Question 46

Which distribution is used in a Z-test? A) Normal distribution B) t-distribution C) Chi-square distribution D) Exponential distribution

Answer 46

Normal distribution

Question 47

In hypothesis testing, if the confidence interval includes zero, this suggests: A) The null hypothesis should be rejected B) There is no significant difference C) The sample mean is larger than the population mean D) The test is invalid

Answer 47

There is no significant difference

Question 48

A two-tailed test is used when: A) The test only evaluates one direction B) The test evaluates two directions C) The test is less powerful D) The test has more Type I errors

Answer 48

The test evaluates two directions

Question 49

What is an effect size in hypothesis testing? A) The probability of making a Type I error B) The size of the effect of interest C) The size of the sample D) The amount of Type II error

Answer 49

The size of the effect of interest

Question 50

If the sample size increases, the p-value will: A) Increase B) Decrease C) Stay the same D) Be zero

Answer 50

Increase

Question 51

The t-test is suitable for: A) Testing the difference between means B) Testing the relationship between variables C) Testing frequencies D) Testing variances

Answer 51

Testing the difference between means

Question 52

When conducting a test for proportions, which condition must be met? A) np ≥ 10 and n(1 − p) ≥ 10 B) np < 5 C) n > 30 D) n(1 − p) < 5

Answer 52

np ≥ 10 and n(1 − p) ≥ 10

Question 53

An increase in sample variance will: A) Increase power B) Increase Type I error C) Decrease power D) Decrease significance level

Answer 53

Decrease power

Question 54

Which of the following tests compares observed frequencies to expected frequencies? A) Paired t-test B) Chi-square test C) Z-test D) Mann-Whitney U test

Answer 54

Chi-square test