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A pharmaceutical company claims their new drug reduces blood pressure by an average of 10 mmHg. A researcher tests this claim with a sample of 25 patients and finds a mean reduction of 8.5 mmHg with a standard deviation of 3 mmHg. What is the correct null hypothesis for this test?

In hypothesis testing, if we reject a true null hypothesis, what type of error have we committed?

A quality control manager tests whether a production process is operating correctly (H₀: process is in control). If the manager fails to detect when the process is actually out of control, what type of error has occurred?

A researcher conducts a hypothesis test with α = 0.05 and obtains a p-value of 0.03. What should be the conclusion?

Which of the following represents a two-tailed test?

A car manufacturer claims their vehicles average 30 mpg. A consumer group tests 36 cars and finds a mean of 28.5 mpg with a population standard deviation of 3 mpg. What is the calculated z-score for this test?

For the car mpg test with z = -3.0 and α = 0.05 (two-tailed), what is the correct decision?

A company claims their batteries last at least 100 hours. A sample of 25 batteries has a mean life of 98 hours with a standard deviation of 5 hours. What type of test should be conducted?

For the battery test with n=25, x̄=98, s=5, and H₀: μ ≥ 100, what is the calculated t-statistic?

If the critical t-value for the battery test (α=0.05, df=24) is -1.711, what should be the conclusion?

A researcher wants to compare the effectiveness of two teaching methods. Method A (n=30) has mean score=78, s=8. Method B (n=35) has mean score=82, s=7. What is the correct null hypothesis?

For the teaching methods comparison, if we assume equal variances, what is the pooled standard deviation?

What is the degrees of freedom for the two-sample t-test assuming equal variances?

A poll shows 120 out of 200 voters support Candidate A. Test the claim that more than 50% support Candidate A. What is the test statistic?

For the candidate support test with z=2.83 and α=0.05 (one-tailed), what is the conclusion?

In a paired t-test, 10 students took a pre-test and post-test. The mean difference (post-pre) was 5 points with standard deviation of differences = 3. What is the t-statistic to test if the improvement is significant?

For the paired t-test with t=5.27, df=9, and α=0.01 (two-tailed), what is the conclusion?

A sample of 15 items has variance 25. Test H₀: σ² = 20 vs H₁: σ² > 20. What is the chi-square statistic?

For the variance test with χ²=17.5, df=14, and α=0.05, what is the conclusion?

Two machines produce components. Machine A: n=10, s²=0.02. Machine B: n=8, s²=0.03. Test H₀: σ₁² = σ₂² vs H₁: σ₁² ≠ σ₂². What is the F-statistic?

For the variance ratio test with F=1.50, df₁=7, df₂=9, and α=0.05, what is the conclusion?

A company claims their light bulbs last 1000 hours. A sample of 30 bulbs has mean 980 hours with population standard deviation 50 hours. What is the p-value for this test?

If α=0.05 and p-value=0.0286, what should be the decision?

A researcher wants to test if a new teaching method improves scores. Which test is most appropriate?

In hypothesis testing, what does the power (1-β) represent?

Which factor does NOT increase the power of a test?

A 95% confidence interval for μ is (48.2, 51.8). What can be concluded about H₀: μ = 50 vs H₁: μ ≠ 50 at α=0.05?

If a 95% CI for the difference between two means is (-2.1, 0.8), what can be concluded about H₀: μ₁ = μ₂?

A company tests H₀: μ = 100 vs H₁: μ ≠ 100 with α=0.05. The p-value is 0.06. What is the conclusion?

What is the main difference between z-test and t-test?

When should we use a two-sample t-test with unequal variances?

A study finds a p-value of 0.001. What does this mean?

Which test is appropriate for comparing variances of two normal populations?

A researcher conducts 20 independent tests at α=0.05. What is the probability of at least one Type I error?

What is the purpose of Bonferroni correction?

A test has power 0.80 to detect an effect size of 0.5. What is β?

Which statement about statistical significance and practical significance is TRUE?

When should a one-tailed test be used?

What is the effect of increasing sample size on hypothesis testing?

A manufacturer claims their tires last 50,000 miles. A consumer group tests 40 tires and finds mean 48,500 miles with standard deviation 4,000 miles. What is the appropriate test?

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