Inferential Statistics: Hypothesis Testing, Confidence Intervals, and P-Values

Question 1

In hypothesis testing, which step involves defining the parameters to be tested and their expected values?

Accepted Answer

State the null and alternative hypotheses

Answer

Calculate the sample mean

Answer

Collect data

Answer

Draw a conclusion

Question 2

A confidence interval is a range that has a specific probability of containing which value?

Accepted Answer

The population parameter of interest

Answer

The sample mean

Answer

The standard error of the mean

Answer

The associated z-score

Question 3

When using the normal distribution for hypothesis testing, what is a key requirement?

Accepted Answer

The sample size is sufficiently large (n > 30) or the population is normally distributed

Answer

The sample size is small (n < 30)

Answer

The population variance is known

Question 4

Which scenario represents a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is actually true

Answer

Failing to reject the null hypothesis when it is false

Answer

Accepting the null hypothesis when it is true

Question 5

Which measure is NOT a representation of the central tendency of a dataset?

Accepted Answer

Range

Answer

Mode

Answer

Median

Answer

Mean

Question 6

What is the fundamental difference between a population and a sample in statistical inference?

Accepted Answer

A population encompasses the entire group of interest, while a sample is a subset representing the population

Answer

A population is more representative than a sample

Answer

A sample is always smaller than a population

Question 7

Which statistical test is commonly used to compare the means of two independent groups?

Accepted Answer

Two-sample t-test

Answer

Paired t-test

Answer

Linear regression

Answer

Pearson correlation coefficient

Question 8

What is a key limitation of inferential statistics?

Accepted Answer

They provide generalizations about the population based on sample data, not absolute certainty

Answer

They can only be applied to large datasets

Answer

They are always prone to bias

Question 9

Which of the following is a type of inferential statistic used to test a hypothesis about a population mean?

Accepted Answer

Z-test

Answer

Percentile

Answer

Mean

Answer

Standard deviation

Question 10

In hypothesis testing, what is the most commonly used level of significance?

Accepted Answer

0.05

Answer

0.10

Answer

0.01

Question 11

What does a p-value less than 0.05 indicate in hypothesis testing?

Accepted Answer

The null hypothesis is rejected in favor of the alternative hypothesis.

Answer

The data is inconclusive.

Answer

The null hypothesis is accepted.

Question 12

What is the purpose of a power analysis in hypothesis testing?

Accepted Answer

To determine the minimum sample size needed to achieve a desired statistical power.

Answer

To calculate the probability of making a Type I error.

Answer

To estimate the effect size of the study.

Question 13

What is the primary function of a confidence interval?

Accepted Answer

To estimate the population mean with a specified level of confidence.

Answer

To test a hypothesis about a population parameter.

Answer

To calculate the probability of a Type I error.

Question 14

What is the difference between a Type I error and a Type II error in hypothesis testing?

Accepted Answer

A Type I error is a false positive, while a Type II error is a false negative.

Answer

A Type II error is a false positive, while a Type I error is a true negative.

Answer

A Type I error is a false positive, while a Type II error is a true positive.

Question 15

Which step initiates the hypothesis testing process?

Accepted Answer

Formulating the research and null hypotheses

Answer

Collecting data

Answer

Calculating the test statistic

Question 16

What is the standard symbol used to represent the null hypothesis?

Accepted Answer

H0

Answer

Ha

Answer

H1

Answer

H

Question 17

If the p-value is smaller than the alpha level, it indicates:

Accepted Answer

Rejection of the null hypothesis

Answer

Acceptance of the null hypothesis

Answer

Acceptance of the alternative hypothesis

Answer

Rejection of the alternative hypothesis

Question 18

What is the primary purpose of a confidence interval?

Accepted Answer

Estimating the population parameter

Answer

Testing the significance of group differences

Answer

Predicting future events

Answer

Determining the p-value

Question 19

Explain the distinction between a type I error and a type II error.

Accepted Answer

Type I error: Incorrect rejection of true null hypothesis; Type II error: Incorrect acceptance of false null hypothesis

Answer

Type I error: Incorrect acceptance of true null hypothesis; Type II error: Incorrect rejection of false null hypothesis

Question 20

What advantage do inferential statistics provide?

Accepted Answer

Generalizing research findings to wider populations

Answer

Eliminating sampling error

Answer

Providing an exact value for the population parameter

Question 21

If the significance level is set at 0.05, what is the probability of committing a type I error?

Accepted Answer

0.05

Answer

0.10

Answer

0.01

Answer

0.95

Question 22

Which characteristic is NOT a parameter of a population?

Accepted Answer

Sample size

Answer

Variance

Answer

Mean

Answer

Standard deviation

Question 23

What is the primary purpose of constructing a confidence interval?

Accepted Answer

To estimate the true population parameter with a specified level of confidence

Answer

To describe the sample data

Answer

To test a hypothesis

Question 24

In hypothesis testing, what does the null hypothesis represent?

Accepted Answer

The claim that there is no significant difference between the parameters

Answer

The claim that the sample mean is equal to the population mean

Answer

The claim that there is a significant difference between the parameters

Question 25

What information does a p-value provide in a hypothesis test?

Accepted Answer

The probability of obtaining the observed sample results, assuming the null hypothesis is true

Answer

The probability of committing a Type I error

Answer

The probability of obtaining the observed sample results, assuming the alternative hypothesis is true

Question 26

Which limitation is inherent to inferential statistics?

Accepted Answer

Inferences can only be made about the population from which the sample was drawn

Answer

Causal relationships can be established

Answer

Precise predictions about future outcomes can be made

Question 27

What is the distinction between a Type I error and a Type II error?

Accepted Answer

A Type I error occurs when the null hypothesis is rejected although it is true, while a Type II error occurs when the null hypothesis is accepted although it is false

Answer

A Type I error occurs when the alternative hypothesis is rejected although it is true, while a Type II error occurs when the alternative hypothesis is accepted although it is false

Question 28

What is a key advantage of using inferential statistics?

Accepted Answer

It allows for generalizations about a population based on a sample

Answer

Hypotheses can be proven with certainty

Answer

Future outcomes can be predicted precisely

Question 29

How does the sample size impact inferential statistics?

Accepted Answer

Larger sample sizes lead to more accurate inferences about the population

Answer

Larger sample sizes lead to less accurate inferences about the population

Answer

Sample size has no effect on the accuracy of inferences about the population

Question 30

What is the fundamental difference between a parameter and a statistic?

Accepted Answer

Parameters describe populations, while statistics describe samples

Answer

Parameters describe samples, while statistics describe populations

Question 31

In a hypothesis test, what is the appropriate null hypothesis for determining if a new teaching method improves student test scores?

Accepted Answer

The average test scores using the new method are equal to the average test scores using the old method.

Answer

The average test scores using the new method are higher than the average test scores using the old method.

Answer

The average test scores using the new method are lower than the average test scores using the old method.

Question 32

Which of the following accurately describes a p-value?

Accepted Answer

It represents the likelihood of obtaining a test statistic that is as extreme as or more extreme than the one observed, assuming the null hypothesis is true.

Answer

It represents the likelihood that the null hypothesis is true.

Question 33

A researcher is conducting a hypothesis test at the 5% level of significance. The p-value for the test is 0.06. What should the researcher conclude?

Accepted Answer

Fail to reject the null hypothesis.

Answer

Lower the level of significance.

Answer

Reject the null hypothesis.

Answer

Increase the sample size.

Question 34

A common source of bias in statistical studies is:

Accepted Answer

Selection bias

Answer

Random error

Answer

Measurement error

Answer

Sampling error

Question 35

Which statistical test is most suitable for comparing the mean test scores of two distinct groups of students?

Accepted Answer

Two-sample t-test

Answer

ANOVA

Answer

Correlation analysis

Answer

Chi-square test

Question 36

In a multiple regression model used to predict employee salaries, what action would increase its explanatory power?

Accepted Answer

Incorporating more independent variables

Answer

Transforming the dependent variable.

Answer

Removing outliers from the data.

Answer

Increasing the sample size.

Question 37

A limitation of using a statistical model for prediction is that:

Accepted Answer

It may not be applicable to new and unseen data.

Answer

It may be too complex.

Answer

It may be biased.

Question 38

A sample of 100 students is drawn randomly from a population of 10,000 students to estimate the mean height of all students in the population. The sample mean height is found to be 170 cm with a sample standard deviation of 10 cm. Assuming that the population is approximately normally distributed, what is the margin of error for the 95% confidence interval for the population mean height?

Accepted Answer

1.96 cm

Answer

2.58 cm

Answer

0.98 cm

Answer

4.98 cm

Question 39

A survey was conducted to determine the average amount of time students spend on social media per day. A sample of 100 students was taken and the sample mean was found to be 90 minutes, with a sample standard deviation of 20 minutes. Assuming a 95% confidence level and that the population is approximately normally distributed, what are the upper and lower bounds for the population mean?

Accepted Answer

(81.35 minutes, 98.65 minutes)

Answer

(80.31 minutes, 99.69 minutes)

Answer

(83.31 minutes, 96.69 minutes)

Answer

(82.35 minutes, 97.65 minutes)

Question 40

Which of the following is the most important assumption of hypothesis testing?

Accepted Answer

The sample is randomly selected from the population.

Answer

The sample size is large.

Answer

The population is normally distributed.

Question 41

Which of the following is the alternative hypothesis in a hypothesis test?

Accepted Answer

The hypothesis that there is a significant difference or relationship.

Answer

The hypothesis that there is no significant difference or relationship.

Answer

The hypothesis that the sample mean is equal to the population mean.

Question 42

Which of the following is NOT a type of inferential statistic?

Accepted Answer

Mean

Answer

P-value

Answer

Hypothesis testing

Answer

Confidence interval

Question 43

What is the purpose of a hypothesis test?

Accepted Answer

To determine whether there is evidence to reject the null hypothesis.

Answer

To estimate a population parameter.

Answer

To make predictions about a population.

Question 44

What is the null hypothesis in a hypothesis test?

Accepted Answer

The hypothesis that there is no difference between the two groups.

Answer

The hypothesis that the first group is greater than the second group.

Answer

The hypothesis that the second group is greater than the first group.

Question 45

What is the alternative hypothesis in a hypothesis test?

Accepted Answer

The hypothesis that there is a difference between the two groups.

Answer

The hypothesis that the second group is greater than the first group.

Answer

The hypothesis that the first group is greater than the second group.

Question 46

What is the p-value of a hypothesis test?

Accepted Answer

The probability of obtaining the observed results or more extreme results, assuming the null hypothesis is true.

Answer

The probability of rejecting the null hypothesis when it is true.

Question 47

What is a confidence interval?

Accepted Answer

A range of values that is likely to contain the true population parameter.

Answer

A hypothesis about the population parameter.

Answer

A single value that is the best estimate of the population parameter.

Question 48

What is the level of confidence of a confidence interval?

Accepted Answer

The probability that the true population parameter is within the confidence interval.

Answer

The probability of rejecting the null hypothesis when it is true.

Answer

The probability of accepting the null hypothesis when it is false.

Question 49

What is the margin of error of a confidence interval?

Accepted Answer

Half the width of the confidence interval.

Answer

The probability of making a Type I error.

Answer

The probability of rejecting the null hypothesis when it is true.

Answer

The probability of accepting the null hypothesis when it is false.

Question 50

Which of the following is NOT an assumption of inferential statistics?

Accepted Answer

The population is normally distributed.

Answer

The sample is random.

Answer

The sample is large enough.

Answer

The data is independent.