Question 1

A researcher conducts a repeated measures ANOVA to test whether the route of anti-nausea medication (IV, sublingual, transdermal) affects symptom relief in 12 oncology patients. The sum of squares between groups (SSB) is 2.8, and the sum of squares within groups (SSW) is 19.4. What is the calculated F-statistic for this study?

Accepted Answer

$$F = \frac{1.40}{0.88} = 1.59$$

Question 2

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true

Question 3

A study finds a statistically significant difference in BMI between two groups with $$p = 0.03$$, but the effect size is $$d = 0.10. $$What is the most appropriate interpretation?

Accepted Answer

The difference is statistically significant but likely not practically meaningful

Question 4

If a 95% confidence interval for the difference in means between two groups is $$(-1.94, 2.44)$$, what can you conclude?

Accepted Answer

No significant difference exists between the groups

Question 5

A clinical trial tests a new pain medication and finds a mean reduction of 0.4 points on a 10-point scale ($$p \u003c 0.001) in 8$$,000 patients. The minimal clinically important difference (MCID) is 2 points. What is the correct interpretation?

Accepted Answer

The result is statistically significant but not clinically meaningful

Question 6

Which formula correctly calculates the standard error of the mean (SEM) for a sample with standard deviation $$s$$ and sample size $$n$$?

Accepted Answer

$$SEM = \frac{s}{\sqrt{n}}$$

Question 7

A study compares the proportion of heart attacks in two groups: Placebo ($$\hat{p}_1 = 0.017) $$and Aspirin ($$\hat{p}_2 = 0.009$$), with a 95% CI for the difference of $$(0.0051, 0.0109). $$What does this CI indicate?

Accepted Answer

Aspirin significantly reduces heart attack risk compared to placebo

Question 8

What is the main risk of conducting multiple t-tests on the same dataset without correction?

Accepted Answer

Increased risk of Type I errors

Question 9

Which of the following is true about effect sizes?

Accepted Answer

Effect sizes quantify the magnitude of a difference, not just its statistical significance

Question 10

A one-sample t-test is performed to compare the mean VO2max of 50 women in 2024 ($$\bar{x} = 3.45$$, $$s = 0.65) to $$the 1964 value ($$\mu_0$ = 3.25). $$The 95% CI for the mean is $$(3.27, 3.63). $$What does this CI tell you?

Accepted Answer

The 1964 value is outside the plausible range for 2024, so the means are significantly different

Question 11

Which of the following best describes statistical power?

Accepted Answer

The probability of correctly rejecting the null hypothesis when it is false

Question 12

In a chi-square goodness-of-fit test, the expected counts for three categories are 90, 70, and 40. The observed counts are 60, 80, and 60. What is the chi-square statistic for the 'Meets guidelines' category?

Accepted Answer

$$\$$chi^2$$ = \frac{(60-90)^2$}{90} = 10.00$$

Question 13

Which of the following is NOT a reason to report effect sizes along with p-values?

Accepted Answer

Effect sizes show the probability of a Type I error

Question 14

A 95% confidence interval for the difference in proportions between two groups is $$(-0.03, 0.04). $$What does this interval suggest?

Accepted Answer

No significant difference exists between the groups

Question 15

Which of the following statements about confidence intervals is correct?

Accepted Answer

If the 95% CI for a mean difference excludes 0, the difference is statistically significant at $$\alpha = 0.05$$

Question 16

Which of the following best explains why a large sample size can lead to a statistically significant result even if the effect is very small?

Accepted Answer

Larger samples make it easier to detect even tiny differences as statistically significant

Question 17

A study reports $$p = 0.051$$ for a difference between two treatments. According to conventional standards, how should this result be interpreted?

Accepted Answer

Not statistically significant at $$\alpha = 0.05$$

Question 18

Which of the following is a correct formula for the 95% confidence interval for the difference between two independent means?

Accepted Answer

$$(\bar{x}_1 - \bar{x}_2) \pm (t_{0.025} 	imes SEM)$$

Effect Sizes, Statistical Significance, and Practical Meaning in Business Statistics

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