Hypothesis Testing: Interactive Quizzes for Year 11 Mathematics

Question 1

A one-sample proportion test is conducted to test if the proportion of students who prefer online learning is different from 0.5. What is the alternative hypothesis?

Accepted Answer

H₁: p ≠ 0.5

Answer

H₁: p = 0.5

Answer

H₁: p < 0.5

Answer

H₁: p > 0.5

Question 2

A hypothesis test is conducted with a p-value of 0.07. At a significance level of 0.05, what is the decision?

Accepted Answer

Fail to reject the null hypothesis

Answer

Reject the null hypothesis

Answer

Cannot conclude

Answer

Need more information

Question 3

In a two-tailed hypothesis test, what is the null hypothesis?

Accepted Answer

The population's parameter is not equal to the hypothesized value.

Answer

The population's parameter is equal to the hypothesized value.

Answer

The population's parameter is greater than the hypothesized value.

Answer

The population's parameter is less than the hypothesized value.

Question 4

Which of the following is known as a Type I error?

Accepted Answer

Rejecting the null hypothesis when it's true.

Answer

Accepting the null hypothesis when it's false.

Answer

Rejecting the alternative hypothesis when it's true.

Answer

Accepting the alternative hypothesis when it's false.

Question 5

Which of the following is not a limitation of hypothesis testing?

Accepted Answer

It's always reliable.

Answer

It can be sensitive to outliers.

Answer

It assumes the sample is representative of the population.

Answer

It can be challenging to select the appropriate test statistic.

Question 6

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

Accepted Answer

Write a report.

Answer

Formulate the hypotheses.

Answer

Collect data.

Answer

Analyze the data.

Question 7

What is the typical significance level used in hypothesis testing?

Accepted Answer

0.05

Answer

0.01

Answer

0.10

Answer

0.20

Question 8

The significance level of a test is:

Accepted Answer

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

Answer

The probability of failing to reject the null hypothesis when it is false.

Answer

The desired probability of making a correct decision.

Answer

The probability that the sample data is representative of the population.

Question 9

For a sample of 100 observations with a mean of 52 and a standard deviation of 10, the standard error of the mean is:

Accepted Answer

1

Answer

0.1

Answer

10

Answer

100

Question 10

In hypothesis testing, a Type I error occurs when:

Accepted Answer

The null hypothesis is rejected when it is true.

Answer

The null hypothesis is accepted when it is false.

Answer

The alternative hypothesis is rejected when it is true.

Answer

The test statistic is not significant.

Question 11

The null hypothesis (H0) represents:

Accepted Answer

The assumption of no difference or effect

Answer

The assumption of a difference or effect

Answer

The probability of rejecting H0 is low

Answer

The probability of accepting H0 is high

Question 12

The p-value is:

Accepted Answer

The probability of observing the sample result assuming H0 is true

Answer

The probability of rejecting H0 if it is true

Answer

The probability of accepting H0 if it is false

Answer

The probability of rejecting H0 if it is false

Question 13

Which of the following is a type I error?

Accepted Answer

Rejecting H0 when it is actually true

Answer

Accepting H0 when it is actually false

Answer

Failing to reject H0 when it is actually false

Answer

Rejecting H0 when it is actually false

Question 14

The level of significance (α) is:

Accepted Answer

The probability of making a type I error

Answer

The probability of making a type II error

Answer

The probability of accepting H0 when it is true

Answer

The probability of rejecting H0 when it is false

Question 15

A hypothesis test results in a p-value of 0.06. Assuming α = 0.05, what is the conclusion?

Accepted Answer

Fail to reject H0

Answer

Reject H0

Answer

The result is inconclusive

Answer

The test is invalid

Question 16

Which of the following is a non-parametric test?

Accepted Answer

Mann-Whitney U test

Answer

Z-test (parametric test)

Answer

t-test (parametric test)

Answer

Chi-squared test (parametric test)

Question 17

Hypothesis testing is particularly useful for:

Accepted Answer

Drawing conclusions about a population based on sample data

Answer

Making predictions

Answer

Describing data

Answer

Testing theories

Question 18

For testing if the average height of pupils in a school differs from 170 cm, which null hypothesis is accurate?

Accepted Answer

H0: μ = 170 cm

Answer

H0: μ ≠ 170 cm

Answer

H0: μ > 170 cm

Answer

H0: μ < 170 cm

Question 19

For testing whether the proportion of students preferring online learning is less than 60%, which alternative hypothesis is appropriate?

Accepted Answer

H1: p < 0.6

Answer

H1: p > 0.6

Answer

H1: p ≠ 0.6

Answer

H1: p = 0.6

Question 20

Which advantage does hypothesis testing offer?

Accepted Answer

Drawing inferences about a population from sample data

Answer

Confirming the validity of a hypothesis

Answer

Eliminating uncertainty in statistical analysis

Answer

Forecasting future occurrences

Question 21

In hypothesis testing, what is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true

Answer

Accepting the null hypothesis when it is false

Answer

Failing to reject the null hypothesis when it is false

Answer

Accepting the alternative hypothesis when it is false

Question 22

A researcher aims to determine if the mean IQ score of a student group differs significantly from 100. Which statistical test is appropriate?

Accepted Answer

One-sample t-test

Answer

Two-sample t-test

Answer

Chi-square test

Answer

F-test

Question 23

Which of the following is a type I error?

Accepted Answer

Rejecting a true null hypothesis

Answer

Accepting a false null hypothesis

Answer

Calculating an incorrect test statistic

Answer

Drawing an invalid conclusion

Question 24

The p-value represents:

Accepted Answer

The probability of obtaining the observed results if the null hypothesis is true

Answer

The probability of obtaining the observed results if the alternative hypothesis is true

Answer

The level of significance of the test

Answer

The effect size of the treatment

Question 25

In a two-sample t-test, the degrees of freedom are calculated as:

Accepted Answer

n1 + n2 - 2

Answer

n1 - n2

Answer

n1 * n2

Answer

n1 / n2

Question 26

A confidence interval for a population proportion is calculated using:

Accepted Answer

The sample proportion plus or minus the margin of error

Answer

The sample proportion multiplied by the margin of error

Answer

The margin of error divided by the sample proportion

Answer

The sample proportion minus the margin of error

Question 27

In a research study, the researcher finds a statistically significant difference between two groups. This means that:

Accepted Answer

The difference between the groups is unlikely to be due to chance

Answer

The difference between the groups is definitely due to the treatment

Answer

The sample size was probably too small

Answer

The results are not meaningful

Question 28

In hypothesis testing, what is the correct sequence of steps?

Accepted Answer

Formulate hypotheses, Collect data, Conduct a test, Draw conclusions

Answer

Collect data, Formulate hypotheses, Conduct a test, Draw conclusions

Answer

Conduct a test, Formulate hypotheses, Collect data, Draw conclusions

Answer

Draw conclusions, Formulate hypotheses, Collect data, Conduct a test

Question 29

When the population standard deviation is known, which test statistic is used?

Accepted Answer

Z-test

Answer

T-test

Answer

Chi-squared test

Answer

F-test

Question 30

What is the purpose of a power analysis?

Accepted Answer

To determine the minimum sample size needed for a given effect size

Answer

To calculate the p-value of a hypothesis test

Answer

To determine the statistical significance of a result

Answer

To analyze the strength of a statistical relationship

Question 31

Which of the following is the initial step in hypothesis testing?

Accepted Answer

Formulate hypotheses

Answer

Collect sample data

Answer

Conduct a statistical test

Answer

Draw conclusions

Question 32

A null hypothesis suggests that:

Accepted Answer

There is no substantial difference between the sample and population.

Answer

The sample data is statistically significant.

Answer

The sample data lacks statistical significance.

Answer

The population mean is identical to the sample mean.

Question 33

In a two-tailed test, the critical values are located at:

Accepted Answer

The extremes of the distribution

Answer

The center of the distribution

Answer

The 25th and 75th percentiles of the distribution

Answer

The 50th percentile of the distribution

Question 34

A p-value of 0.01 implies that:

Accepted Answer

The null hypothesis is rejected at the 1% significance level.

Answer

The null hypothesis is accepted at the 1% significance level.

Answer

The sample data is statistically significant.

Answer

The population mean is significantly different from the sample mean.

Question 35

In a one-sample t-test, the t-statistic is calculated as:

Accepted Answer

t = (x̄ - μ) / (s / √n)

Answer

t = (μ - x̄) / (s / √n)

Answer

t = (x̄ - μ) / (s √n)

Answer

t = (μ - x̄) / (s √n)

Question 36

Hypothesis testing is a valuable statistical tool because it:

Accepted Answer

Facilitates inferences about a population based on sample data.

Answer

Guarantees that the conclusions are always correct.

Answer

Eliminates the need for data collection.

Answer

Is an overly complex and inaccessible method.

Question 37

Which is the initial step in hypothesis testing?

Accepted Answer

Formulation of hypotheses

Answer

Data collection

Answer

Result analysis

Answer

Conclusion drawing

Question 38

In hypothesis testing, what is the null hypothesis?

Accepted Answer

The hypothesis assumed to be true unless proven otherwise

Answer

The contrasting hypothesis

Answer

The research hypothesis

Answer

The hypothesis being tested

Question 39

Which is an example of a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true

Answer

Accepting the null hypothesis when it is false

Answer

Failing to reject the null hypothesis when it is false

Answer

Accepting the alternative hypothesis when it is true

Question 40

Which of the following is not a trait of a good hypothesis?

Accepted Answer

Complex

Answer

Testable

Answer

Falsifiable

Answer

Precise

Question 41

Which of the following is an example of a research question suitable for hypothesis testing?

Accepted Answer

Is there a height difference between male and female students?

Answer

What is the favorite color among teenagers?

Answer

How many students in this class play video games?

Answer

What's the optimal method for learning mathematics?

Question 42

Which of the following is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is **actually true**.

Answer

Accepting the null hypothesis when it is false.

Answer

Failing to reject the null hypothesis when it is false.

Answer

Rejecting the alternative hypothesis when it is true.

Question 43

Which of the following is a one-tailed test?

Accepted Answer

A test that has a rejection region in **one tail** of the distribution.

Answer

A test that has a rejection region in both tails of the distribution.

Answer

A test that has no rejection region.

Answer

A test that uses a sample size of one.

Question 44

If the p-value is less than the significance level, we can conclude that:

Accepted Answer

Reject the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

The test is inconclusive

Answer

The alternative hypothesis is false

Question 45

A researcher wants to test whether the average weight of children in a town is different from 20 kg. Which of the following hypotheses should be used?

Accepted Answer

H₀: μ = 20, H₁: μ ≠ 20

Answer

H₀: μ ≥ 20, H₁: μ < 20

Answer

H₀: μ ≤ 20, H₁: μ > 20

Answer

H₀: μ ≠ 20, H₁: μ = 20