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Suppose the original test uses a one-tailed significance level of α=0.05\alpha=0.05. The researcher reduces the significance level to α=0.01\alpha=0.01, while the sample size, effect size and population variability remain unchanged.

Which panel (A to D) correctly represents the resulting distributions and decision rule?

Suppose the following plot represents the sampling distribution of a test statistic under two competing hypotheses. The red curve shows the distribution when the null hypothesis, H0H_0, is true, while the blue curve shows the distribution when the alternative hypothesis, H1H_1, is true. The dashed line represents the critical value for a one-tailed hypothesis test. If the test statistic falls to the right of this critical value, H0H_0 is rejected.

The shaded regions represent the two types of errors that may occur when making a hypothesis-testing decision.

Which conditional probability represents the red shaded region?

A study investigated whether face-to-face students achieve higher exam scores than online students. A one-tailed Welch two-sample tt-test produced a pp-value of 0.032.

Which statement is the most appropriate interpretation of this pp-value?

A study investigated whether the population mean exam score differs between Engineering and Business students. A two-tailed Welch two-sample tt-test produced a pp-value of 0.083. The test was conducted using a significance level of α=0.05\alpha=0.05.

Which statement provides the most appropriate interpretation and conclusion?

Consider the plot provided in Q16. 

Suppose the sample size is increased while the effect size and significance level remain unchanged. As a result, both sampling distributions become narrower, but their centres remain in the same locations. Based on the plot, what is the most likely consequence?

The university claims that the population mean exam score is 70. Conduct an appropriate statistical test to determine whether the population mean exam score differs from 70, irrespective of school. Test with a significance level of 1%.

Which of the statements below is correct?

Conduct an appropriate statistical test to determine whether there is a significant difference (let the significance level = 1%) between Science and Arts students for mean exam score.

What is the p-value for this test? Round your answer to 2 decimal places.

The university considers an average Week 8 test score above 65 to indicate satisfactory progress. Conduct an appropriate statistical test to determine whether there is evidence that the population mean Week8 test score is greater than 65, irrespective of school. Test with a significance level of 1%.

Conduct an appropriate statistical test to determine whether students’ population mean test score increased between Week 4 and Week 8, for those from the IT school only.

Define the difference as: Week8 - Week4.

What is the computed p-value, rounded to 3 decimal places?