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(a) When performing a test of significance for a null hypothesis, H0 against an alternative hypothesis HA, the p-value is:

(i) The probability that H0 is true given the sample data

(ii) The probability that HA is true given the sample data

(iii) The probability of observing a sample result at least as extreme as that observed if H0 is true

(iv) The probability of observing a sample result at least as extreme as that observed if HA is true

(b) A 95% confidence interval for the (unknown) population proportion is 0.62 to 0.68. This means that:

(i) Ninety-five percent of the population lie between 0.62 and 0.68.

(ii) If we repeat the study over and over again, 95% of the resulting confidence intervals will contain the population proportion.

(iii) If we repeat the study over and over again, 95% of the times the population proportion will lie between 0.62 and 0.68.

(iv) If we repeat the study over and over again, 95% of the resulting confidence intervals will contain the sample proportion.

(c) A researcher wishes to obtain 600 patients requiring an operation for acute appendicitis. Three hundred (300) of them are to receive the standard anesthetic (A) and the remainder, an experimental anesthetic (B), which, it is hoped, will reduce the recovery time. She knows that randomization can help in greatly reducing the effects of confounding variables in this kind of experiment.

Which of the following statement is the closest to the truth?

(i) Selecting a random sample of such patients will substantially equalize the distribution of confounding variables over the two treatment groups. 

(ii) Matching the two groups on several of the likely confounding variable will substantially equalize the distribution of confounding variables over the two treatment groups. 

(iii) Only randomly selecting the patients and then randomly assigning them to the two treatments will substantially equalize the distribution of confounding variables over the two treatment groups. 

(iv) Randomly assigning the 600 patients to the two treatment groups will substantially equalize the distribution of confounding variables over the two treatment groups.

(d) A recent editorial in the New York Times reported on a clinical trial in which two different drugs for treating breast cancer in older women were compared. The editorial contained the phrase "The difference fell just shy of statistical significance, so it remains possible that it occurred by chance, ..." Which of the following possible p-values is the most consistent with this phrase?

(i)  p-value = 0.46

(ii) p-value = 0.046

(iii) p-value = 0.064

(iv) p-value = 0.64

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