Question 1

A clinical trial tests whether a new drug reduces cholesterol. The null hypothesis is $$H_0$$: \mu = 0$$ (no effect), and the alternative is H_a$$: \mu \u003c 0$$ (drug reduces cholesterol). The trial finds a sample mean reduction of -12$ mg/dL, with a P$-value of 0.03$. What is the correct interpretation?

Accepted Answer

There is statistically significant evidence at the 5% level that the drug reduces cholesterol.

Question 2

A researcher finds a correlation coefficient $$r = 0.98$$ between ice cream sales and drowning incidents. Which of the following best explains why this does not imply causation?

Accepted Answer

There is likely a lurking variable, such as temperature, that affects both ice cream sales and drowning incidents.

Question 3

In a study, the regression equation for predicting systolic blood pressure ($$y) $$from age ($$x) is$$ $$y = 90 + 0.5x. $$What is the predicted systolic blood pressure for a 60-year-old?

Accepted Answer

$$y = 150$$

Question 4

A hospital administrator uses Benford’s Law to check for fraud in billing data. Which of the following is a correct application of Benford’s Law?

Accepted Answer

Comparing the observed frequency of leading digits to the expected frequencies given by Benford’s Law.

Question 5

A 2×2 table from a clinical trial shows the following: 80 patients received Tamiflu, 60 recovered; 80 received placebo, 40 recovered. What is the recovery rate for the Tamiflu group?

Accepted Answer

$$\frac{60}{80} = 0.75$$

Question 6

A scatterplot of heights and arm spans for 100 adults shows two distinct clusters: one for males and one for females. What effect does this clustering have on the correlation coefficient $$r$$?

Accepted Answer

It can inflate or deflate $$r$$, making it misleading about the relationship within each group.

Question 7

A researcher uses a regression line based on data for cricket chirps between 882 and 1200 per minute to predict the temperature for 3000 chirps per minute. Why is this prediction unreliable?

Accepted Answer

It is an extrapolation far outside the observed data range, where the relationship may not hold.

Question 8

In an ANOVA test comparing mean pulse rates across three age groups of women, the $$P-$$value is $$0.002. $$What is the correct conclusion at the 5% significance level?

Accepted Answer

There is a statistically significant difference in mean pulse rates among the age groups.

Question 9

A 2×2 table for a COVID-19 vaccine trial shows: 20,000 vaccinated, 50 cases; 20,000 unvaccinated, 500 cases. What is the relative risk of infection for the vaccinated group compared to the unvaccinated group?

Accepted Answer

$$\frac{50/20000}{500/20000} = 0.1$$

Question 10

A study finds $$r = 0.066$$ and $$P-$$value $$= 0.428$$ for the relationship between two variables. What does this imply about using the regression equation for prediction?

Accepted Answer

The regression equation should not be used because the relationship is not statistically significant.

Question 11

A polygraph test for detecting lies has a sensitivity of 80% and a specificity of 90%. If 10% of the tested population are actually lying, what is the probability that a person who tests positive is actually lying? (Assume 1000 people tested.)

Accepted Answer

About 47%

Question 12

A researcher tests whether the distribution of eye colors in a sample matches the expected proportions from a theoretical model. Which statistical test is most appropriate?

Accepted Answer

Chi-square goodness-of-fit test

Question 13

In a study of the effect of motorcycle helmet color on injury rates, a 2×5 contingency table is analyzed. What is the main advantage of using a chi-square test in this context?

Accepted Answer

It allows comparison of injury rates across multiple helmet colors simultaneously.

Question 14

A study finds a strong correlation ($$r = 0.95) $$between cheese consumption and engineering PhDs awarded. Why is it inappropriate to use the regression line for prediction in this case?

Accepted Answer

The correlation is likely spurious due to a lurking variable, not a causal relationship.

Question 15

A clinical trial for a new treatment uses a 2×2 table and finds no significant association between treatment and outcome ($$P-$$value $$= 0.62). $$What is the correct interpretation?

Accepted Answer

There is no statistically significant evidence that the treatment affects the outcome.

Question 16

A researcher wants to test if the number of bomb hits in different regions of London during WWII fits a Poisson distribution. Which test should be used?

Accepted Answer

Chi-square goodness-of-fit test

Question 17

A study compares measured and self-reported weights for a group of females. Which statistical method is most appropriate to test if there is a significant difference between the two sets of values?

Accepted Answer

Paired $$t-$$test

Question 18

A clinical trial for a new vaccine finds a $$P-$$value $$\u003c 0.0001$$ for the difference in infection rates between vaccinated and unvaccinated groups. What does this imply?

Accepted Answer

There is extremely strong evidence that the vaccine is effective.

Question 19

A researcher is testing whether the number of adverse health conditions is associated with having tooth fillings. The $$P-$$value is $$0.78. $$What should the researcher conclude?

Accepted Answer

There is no statistically significant association between tooth fillings and adverse health conditions.

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