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Hypothesis Testing MCQs

Hypothesis Testing MCQs cover how statisticians use sample data to decide whether to reject a claim about a population, including significance levels, errors and the power of a test. This set currently has 1 question, and it shows its correct answer instantly, making it a quick check on a key statistics idea.

Question 01 Hypothesis Testing

If a one-tailed test gives a p-value of 0.02, what would the corresponding two-tailed p-value be for the same symmetric statistic?

Correct answer B. 0.04

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Question 02 Hypothesis Testing

Which test is used to compare the variances of two normal populations?

Correct answer D. F-test

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Question 03 Hypothesis Testing

For H0: μ = 50 against H1: μ ≠ 50, a sample of 36 gives x̄ = 48 with σ = 6. At the 5% level, what is the conclusion?

Correct answer C. Reject H0 since |z| = 2 exceeds 1.96

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Question 04 Hypothesis Testing

A population has standard deviation 12. What is the standard error of the mean for samples of size 36?

Correct answer C. 2

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Question 05 Hypothesis Testing

With all else fixed, which change reduces the probabilities of both Type I and Type II errors?

Correct answer B. Increasing the sample size

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Question 06 Hypothesis Testing

How many degrees of freedom does a one-sample t-test based on 20 observations have?

Correct answer C. 19

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Question 07 Hypothesis Testing

In a sample of 100 voters, 60 favour a proposal. Testing H0: p = 0.5, what is the z statistic for the proportion?

Correct answer C. 2.0

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Question 08 Hypothesis Testing

In hypothesis testing, the set of values of the test statistic that leads to rejection of H0 is called what?

Correct answer A. Critical region

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Question 09 Hypothesis Testing

As the degrees of freedom increase, the t distribution approaches which distribution?

Correct answer C. Standard normal distribution

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Question 10 Hypothesis Testing

A t-test is preferred over a z-test for a mean mainly when which condition holds?

Correct answer A. Sample is small and population standard deviation is unknown

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Question 11 Hypothesis Testing

Which of the following can never be the value of a chi-square statistic?

Correct answer B. A negative number

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Question 12 Hypothesis Testing

A die is rolled 60 times giving faces 1 to 6 with frequencies 8, 12, 9, 11, 10 and 10. What is the chi-square statistic for testing that the die is fair?

Correct answer D. 1.0

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Question 13 Hypothesis Testing

A coin tossed 50 times gives 30 heads and 20 tails. What is the chi-square statistic for testing fairness?

Correct answer C. 2.0

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Question 14 Hypothesis Testing

A chi-square goodness-of-fit test has 6 categories and no parameters estimated from the data. What are its degrees of freedom?

Correct answer B. 5

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Question 15 Hypothesis Testing

A chi-square test of independence uses a contingency table with 3 rows and 4 columns. How many degrees of freedom does it have?

Correct answer D. 6

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Question 16 Hypothesis Testing

In a pooled two-sample t-test with samples of sizes 12 and 10, how many degrees of freedom are used?

Correct answer B. 20

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Question 17 Hypothesis Testing

A sample of 16 observations has mean 105 and standard deviation 10. Testing H0: μ = 100, what is the value of t?

Correct answer B. 2.0

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Question 18 Hypothesis Testing

A sample of 64 items has mean 52. If the population mean under H0 is 50 and σ = 8, what is the value of the z statistic?

Correct answer D. 2.0

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Question 19 Hypothesis Testing

Which statement best describes a p-value?

Correct answer D. Probability of a result at least as extreme as observed, assuming H0 is true

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Question 20 Hypothesis Testing

A test gives a p-value of 0.03. At the 5% level of significance, what is the correct decision?

Correct answer A. Reject the null hypothesis

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About Hypothesis Testing MCQs

Hypothesis testing compares a null hypothesis, usually a statement of no effect, with an alternative hypothesis. The significance level, alpha, is the probability of a Type I error, rejecting a true null hypothesis. Beta is the probability of a Type II error, failing to reject a false null hypothesis, and 1 minus beta is the power of the test. The current question asks how power changes when alpha increases: raising alpha makes rejection easier, so power rises, at the cost of more Type I errors. Related ideas include p-values, test statistics and critical regions.

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Frequently asked questions

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

A Type I error happens when a true null hypothesis is rejected, and its probability is the significance level, alpha. A Type II error happens when a false null hypothesis is not rejected, and its probability is beta. For a fixed sample size, reducing one type of error usually increases the other.

What happens to the power of a test when alpha increases?

When alpha increases, the power of the test, 1 minus beta, also increases, as long as the sample size and true effect stay the same. A larger alpha widens the rejection region, so a false null hypothesis is more likely to be rejected, but the risk of a Type I error also rises.

Last reviewed October 2026