Hypothesis Testing: Master the Fundamentals for Data Analytics

Question 1

Which of the following correctly represents the null hypothesis stating that the population mean μ is equal to 100?

Accepted Answer

H0: μ = 100

Answer

H0: μ ≠ 100

Answer

H1: μ = 100

Answer

H1: μ ≠ 100

Question 2

In hypothesis testing, the significance level (α) serves to:

Accepted Answer

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

Answer

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

Answer

Calculate the p-value of the test.

Answer

Establish the sample size required for the test.

Question 3

A researcher is investigating the effectiveness of a marketing campaign and wishes to determine if it increases sales. Which of the following would be an appropriate alternative hypothesis?

Accepted Answer

H1: μ > 1000

Answer

H1: μ < 1000

Answer

H1: μ = 1000

Answer

H1: μ ≠ 1000

Question 4

If the p-value of a hypothesis test is less than the significance level, which conclusion can be drawn?

Accepted Answer

Reject the null hypothesis.

Answer

Accept the null hypothesis.

Answer

Cannot reject the null hypothesis.

Answer

Cannot accept the alternative hypothesis.

Question 5

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

Accepted Answer

To determine the minimum sample size required to achieve a desired level of power.

Answer

To calculate the p-value of a hypothesis test.

Answer

To determine the significance level of a hypothesis test.

Answer

To estimate the effect size of a study.

Question 6

What is the primary role of a confidence interval in hypothesis testing?

Accepted Answer

To provide an estimate of the true population parameter.

Answer

To test the null hypothesis.

Answer

To determine the significance level.

Answer

Confidence intervals are not used in hypothesis testing.

Question 7

Which research question is best suited for hypothesis testing and allows for clear null and alternative hypotheses?

Accepted Answer

Is there a significant difference in average salaries between male and female employees?

Answer

What is the relationship between job satisfaction and employee productivity?

Answer

How many employees are satisfied with their current benefits?

Question 8

Which of the following precisely defines the null hypothesis?

Accepted Answer

The hypothesis we presume to be accurate until proven otherwise

Answer

The hypothesis we aim to prove

Answer

The hypothesis we believe to be incorrect

Answer

The hypothesis we will accept if the p-value is less than the significance level

Question 9

Which of the following is NOT a step in hypothesis testing?

Accepted Answer

Determine the sample size before collecting data

Answer

State the null and alternative hypotheses

Answer

Collect data

Answer

Calculate the p-value

Question 10

What type of error occurs when we reject the null hypothesis when it is actually valid?

Accepted Answer

Type I error

Answer

Type II error

Answer

Alpha error

Answer

Beta error

Question 11

Which formula calculates the p-value?

Accepted Answer

P-value = Probability of obtaining a test statistic as extreme or more extreme than the observed value

Answer

P-value = (Observed value - Expected value) / Standard deviation

Answer

P-value = Significance level - Observed value

Answer

P-value = 1 - (Observed value / Expected value)

Question 12

What is the critical value?

Accepted Answer

The value of the test statistic that separates the rejection and acceptance regions

Answer

The p-value at which the null hypothesis is rejected

Answer

The significance level

Answer

The difference between the observed and expected values

Question 13

What is the concern surrounding p-hacking in hypothesis testing?

Accepted Answer

It involves selectively reporting results that support a desired hypothesis.

Answer

It is an accepted statistical practice to find significant results.

Answer

It requires collecting data until a statistically significant result is attained.

Answer

It is a method for increasing the power of a hypothesis test.

Question 14

In hypothesis testing, if the calculated p-value is lower than the set significance level (α), what should you conclude about the null hypothesis?

Accepted Answer

Reject the null hypothesis

Answer

Accept the null hypothesis

Answer

Increase the sample size

Question 15

In hypothesis testing, the commonly used significance level (alpha) is:

Accepted Answer

0.05

Answer

0.01

Answer

0.10

Answer

0.15

Question 16

The p-value in hypothesis testing represents:

Accepted Answer

The probability of obtaining the observed result if the null hypothesis (H0) is true.

Answer

The probability of obtaining the observed result if the alternative hypothesis (Ha) is true.

Answer

The probability of rejecting the null hypothesis (H0) if it is true.

Answer

The probability of accepting the alternative hypothesis (Ha) if it is true.

Question 17

The purpose of a power analysis is to:

Accepted Answer

Determine the sample size needed to achieve a desired power.

Answer

Calculate the p-value of a hypothesis test.

Answer

Determine the significance level of a hypothesis test.

Answer

Prove the null hypothesis (H0).

Question 18

The key difference between one-tailed and two-tailed hypothesis tests lies in:

Accepted Answer

The direction of the alternative hypothesis (Ha).

Answer

The level of significance.

Answer

The type of statistical test used.

Answer

The sample size.

Question 19

The role of a confidence interval in hypothesis testing is to:

Accepted Answer

Estimate the population parameter.

Answer

Determine the p-value.

Answer

Reject the null hypothesis (H0).

Answer

Calculate the power of the test.

Question 20

In hypothesis testing for a marketing campaign's impact on sales, which statement accurately represents the null hypothesis (H0)?

Accepted Answer

Sales remain unchanged with the new marketing campaign.

Answer

Sales increase due to the new marketing campaign.

Answer

Sales decline with the new marketing campaign.

Answer

Sales fluctuate unpredictably with the new marketing campaign.

Question 21

In hypothesis testing, what is the most commonly used significance level (alpha)?

Accepted Answer

0.05

Answer

0.005

Answer

0.01

Answer

0.10

Question 22

Which of the listed options is NOT a potential error in hypothesis testing?

Accepted Answer

Type III error

Answer

Type I error

Answer

Type II error

Answer

Sampling bias

Question 23

In hypothesis testing, what does a p-value below the significance level (alpha) indicate?

Accepted Answer

Rejection of the null hypothesis

Answer

Acceptance of the alternative hypothesis

Answer

Insufficient evidence to draw conclusions

Answer

Flawed data analysis

Question 24

Which of the following is an example of a two-tailed hypothesis test?

Accepted Answer

Testing whether the difference between two sample means is statistically significant.

Answer

Testing whether the mean height of students exceeds 6 feet.

Answer

Testing whether the proportion of defective products falls below 5%.

Answer

Testing whether a categorical variable is independent of another categorical variable.

Question 25

What is the initial step in conducting a hypothesis test?

Accepted Answer

Formulating the null and alternative hypotheses

Answer

Collecting data

Answer

Calculating the test statistic

Answer

Interpreting the results

Question 26

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

Accepted Answer

Determining the appropriate sample size to achieve a desired level of statistical power.

Answer

Estimating the effect size that can be detected with a given sample size.

Answer

Calculating the p-value of a hypothesis test.

Answer

Determining the significance level of a hypothesis test.

Question 27

To ensure effective hypothesis testing, what is the correct order of steps?

Accepted Answer

State the research question, formulate hypotheses, collect data, analyze data, draw conclusions

Answer

Formulate hypotheses, collect data, state the research question, analyze data, draw conclusions

Answer

Collect data, formulate hypotheses, state the research question, analyze data, draw conclusions

Question 28

Which of the following is the correct format for a null hypothesis?

Accepted Answer

H0: μ equals 0

Answer

H0: μ is not equal to 0

Answer

H0: μ is greater than 0

Answer

H0: μ is less than 0

Question 29

What is the purpose of a significance level (α)?

Accepted Answer

To determine the probability of rejecting the null hypothesis when it is true (Type I error).

Answer

To determine the probability of accepting the null hypothesis when it is false (Type II error).

Answer

To determine the sample size required for the hypothesis test.

Answer

To determine the p-value for the hypothesis test.

Question 30

A p-value of 0.05 indicates:

Accepted Answer

The null hypothesis should be rejected at a 5% significance level.

Answer

There is a 5% probability that the null hypothesis is true.

Answer

There is a 5% probability that the alternative hypothesis is true.

Answer

The alternative hypothesis should be rejected at a 95% confidence level.

Question 31

What is the difference between a one-tailed and a two-tailed hypothesis test?

Accepted Answer

A one-tailed test tests for a specific direction of difference, while a two-tailed test tests for any direction of difference.

Answer

A two-tailed test tests for a specific direction of difference, while a one-tailed test tests for any direction of difference.

Answer

A one-tailed test requires a larger sample size than a two-tailed test.

Answer

A two-tailed test requires a larger sample size than a one-tailed test.

Question 32

The first step in hypothesis testing involves:

Accepted Answer

Formulating a null and alternative hypothesis

Answer

Collecting and analyzing data

Answer

Calculating a p-value

Answer

Determining a significance level

Question 33

The null hypothesis is typically denoted by:

Accepted Answer

H0

Answer

H1

Answer

α

Answer

β

Question 34

The significance level represents the:

Accepted Answer

Risk of incorrectly rejecting the null hypothesis

Answer

Probability of accepting the null hypothesis when it is false

Answer

Amount of confidence in the test results

Answer

Minimum sample size required

Question 35

A Type II error occurs when:

Accepted Answer

The null hypothesis is accepted when it is false

Answer

The null hypothesis is rejected when it is true

Answer

The significance level is set too low

Answer

The sample size is too small

Question 36

The purpose of a confidence interval in hypothesis testing is to:

Accepted Answer

Provide a range of plausible values for the population parameter

Answer

Determine the significance of the test results

Answer

Estimate the sample size

Answer

Test the null hypothesis

Question 37

In which research scenario would hypothesis testing be an appropriate approach? Provide a brief justification for your choice.

Accepted Answer

Evaluating the effectiveness of a new advertising campaign by comparing its impact on sales figures to a control group

Answer

Predicting customer churn based on historical data

Answer

Analyzing the financial performance of a company over several years to identify trends

Answer

Conducting a survey to gather feedback on a new product launch

Question 38

Which of the following are primary ethical considerations for researchers when conducting hypothesis testing?

Accepted Answer

Maintaining participant confidentiality

Accepted Answer

Obtaining informed consent from participants

Answer

Using a significance level of 0.05

Answer

Ensuring the sample size is large enough

Question 39

A null hypothesis generally states that:

Accepted Answer

There is no substantial difference between the groups being compared.

Answer

The difference between the groups is statistically significant.

Answer

The alternative hypothesis is valid.

Question 40

A p-value is the probability of:

Accepted Answer

Observing a test statistic that is as extreme as, or more extreme than, the one that was observed, assuming the null hypothesis is true.

Answer

Rejecting the null hypothesis

Question 41

Which of the following is defined as rejecting the null hypothesis when it is actually true?

Accepted Answer

Type I error

Answer

Type II error

Answer

Accepting the null hypothesis when it is false

Answer

Rejecting the alternative hypothesis when it is true

Question 42

Which of the following is defined as accepting the null hypothesis when it is actually false?

Accepted Answer

Type II error

Answer

Accepting the null hypothesis when it is true

Answer

Type I error

Answer

Rejecting the alternative hypothesis when it is true

Question 43

A commonly used significance level is:

Accepted Answer

0.05

Answer

0.20

Answer

0.10

Question 44

When the p-value is lower than the significance level, the appropriate action is to:

Accepted Answer

Reject the null hypothesis

Answer

Accept the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

Reject the alternative hypothesis

Question 45

Which of the following is a primary advantage of hypothesis testing?

Accepted Answer

It allows for drawing inferences from data

Answer

It guarantees accurate results

Answer

It is easy to apply

Question 46

In a hypothesis test, the null hypothesis (H0) typically represents:

Accepted Answer

There is no significant difference or effect.

Answer

The second group is superior to the first group.

Answer

The first group is superior to the second group.

Question 47

The p-value in a hypothesis test represents:

Accepted Answer

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

Answer

The probability of rejecting the null hypothesis.

Question 48

Which of the following is a necessary condition for using a two-sample t-test to compare two independent groups?

Accepted Answer

The samples are independent, normally distributed, and have equal variances.

Answer

The samples are dependent, normally distributed, and have equal variances.

Answer

The samples are independent, normally distributed, but have unequal variances.

Question 49

Which of the following is a necessary condition for using a one-way ANOVA to compare more than two groups?

Accepted Answer

The samples are independent, normally distributed, and have equal variances.

Answer

The samples are dependent, normally distributed, and have equal variances.

Answer

The samples are independent, normally distributed, but have unequal variances.

Question 50

A Type I error in hypothesis testing occurs when:

Accepted Answer

The null hypothesis is rejected even though it is true.

Answer

An incorrect test statistic is used.

Answer

The null hypothesis is accepted even though it is false.

Question 51

A Type II error in hypothesis testing occurs when:

Accepted Answer

The null hypothesis is accepted even though it is false.

Answer

Insufficient data is collected.

Answer

The null hypothesis is rejected even though it is true.

Answer

An incorrect test statistic is used.

Question 52

A key advantage of hypothesis testing is that it:

Accepted Answer

Provides a structured approach for making decisions about a population based on sample data.

Answer

Guarantees the correct decision will always be made.

Answer

Eliminates the need for data collection.

Question 53

A limitation of hypothesis testing is that it:

Accepted Answer

Cannot prove the null hypothesis to be true.

Answer

Can only be applied to large sample sizes.

Answer

Is overly complex to understand and implement.

Answer

Is immune to the quality of the data used.

Question 54

When is it appropriate to use a one-tailed hypothesis test?

Accepted Answer

When there is a strong prior belief about the direction of the effect being tested.

Answer

When the sample size is large.

Answer

When there is no prior belief about the direction of the effect being tested.