Q: A geneticist expects a 1:2:1 ratio of phenotypes in a sample of 400 offspring. The observed counts are 110, 210, and 80. What is the expected count for the second phenotype?

$$400 \times \frac{2}{4} = 200$$

Question 1

Which of the following best describes a response variable in the context of hypothesis testing with categorical data?

Accepted Answer

A variable that measures the outcome of interest and is affected by changes in the explanatory variable.

Question 2

In a study examining the effect of a new drug on recovery rates, which is the explanatory variable?

Accepted Answer

The type of drug administered to patients.

Question 3

Which formula is used to calculate the test statistic for a one-sample test for a proportion?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$(1-p_0$)}{n}}}$$

Question 4

A vaccine trial finds that 40 out of 150 participants report side effects. What is the sample proportion of side effects?

Accepted Answer

$$\frac{40}{150} = 0.267$$

Question 5

Which of the following is the correct formula for a confidence interval for a proportion?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 6

When testing for a difference in proportions between two independent samples, which formula is used for the test statistic?

Accepted Answer

$$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1$} + \frac{1}{n_2$})}}$$

Question 7

A company claims that 80% of its customers are satisfied. An independent survey finds 110 out of 150 customers are satisfied. What is the null hypothesis for a one-sample proportion test?

Accepted Answer

$$H_0$$: p = 0.80$$

Question 8

Which formula is used to calculate the expected count for a cell in a chi-square test for association?

Accepted Answer

$$E_{ij} = \frac{R_i C_j}{N}$$

Question 9

In a chi-square goodness of fit test, which formula is used to calculate the test statistic?

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O_i - E_i)^2$}{E_i}$$

Question 10

A geneticist expects a 1:2:1 ratio of phenotypes in a sample of 400 offspring. The observed counts are 110, 210, and 80. What is the expected count for the second phenotype?

Accepted Answer

$$400 	imes \frac{2}{4} = 200$$

Question 11

Which adjustment is used to control the family-wise error rate when constructing multiple confidence intervals in a chi-square analysis?

Accepted Answer

Bonferroni adjustment

Question 12

In a chi-square test for association, what does the alternative hypothesis state?

Accepted Answer

At least one cell has a probability that differs from the product of marginal probabilities.

Question 13

Which formula gives the degrees of freedom for a chi-square test for association in a contingency table with $$r$$ rows and $$c$$ columns?

Accepted Answer

$$(r-1)(c-1)$$

Question 14

A/B testing compares the success rates of two website designs. If 120 out of 200 users prefer design A and 100 out of 200 users prefer design B, what is the pooled proportion for the test statistic?

Accepted Answer

$$\frac{120 + 100}{200 + 200} = 0.55$$

Question 15

Which of the following is a key assumption for using the normal approximation in a one-sample proportion test?

Accepted Answer

$$np_0$$ \geq 10$$ and n(1$$-$$p_0$$) \geq 10$$

Question 16

In a chi-square goodness of fit test, what does a significant result indicate?

Accepted Answer

The observed category frequencies differ significantly from the expected frequencies.

Question 17

Which formula is used to calculate the standard error for the difference in proportions between two independent samples?

Accepted Answer

$$\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1$} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2$}}$$

Hypothesis Testing with Categorical Response: Proportions and Chi-Square Methods

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