Question 1

Which of the following best defines the concept of 'expected counts' in the context of a chi-square test for independence?

Accepted Answer

The number of observations that are predicted by the null hypothesis for each cell in a contingency table.

Question 2

A company tests two versions of a TV commercial in different markets. The observed number of purchases for Version 1 is 100 out of 400, and for Version 2 is 180 out of 450. What is the weighted average proportion of purchases for both versions combined?

Accepted Answer

$$\frac{100 + 180}{400 + 450} = \frac{280}{850} \approx 0.329$$

Question 3

In a survey, the proportion of adults who work at least 40 hours per week is being studied. If 70 out of 100 men and 55 out of 100 women report working at least 40 hours, what is the difference in proportions between men and women?

Accepted Answer

$$\frac{70}{100} - \frac{55}{100} = 0.7 - 0.55 = 0.15$$

Question 4

Which of the following statements about the distribution of sample proportions is correct?

Accepted Answer

The distribution of sample proportions is approximately normal if the sample size is large and both $$np$$ and $$n(1-p)$$ are at least 10.

Question 5

A researcher wants to test if the proportion of people who prefer tea over coffee is different in two cities. Which statistical test should be used?

Accepted Answer

Two-proportion z-test

Question 6

Suppose the null hypothesis for a chi-square test of association is true. What would you expect about the observed and expected counts?

Accepted Answer

The observed counts should be close to the expected counts in each cell.

Question 7

In a chi-square test for independence, which of the following is NOT an assumption that must be met?

Accepted Answer

The data must be normally distributed.

Question 8

A positive test statistic in a two-proportion z-test indicates:

Accepted Answer

The first sample proportion is greater than the second sample proportion.

Question 9

Which formula is used to calculate the standard error for the difference between two sample proportions?

Accepted Answer

$$SE = \sqrt{\frac{p_1$(1-p_1$)}{n_1$} + \frac{p_2$(1-p_2$)}{n_2$}}$$

Question 10

A student claims that the results of a chi-square test are significant at the 0.05 level. What does this mean?

Accepted Answer

There is sufficient evidence to reject the null hypothesis at the 5% significance level.

Question 11

In a real-world scenario, a medical researcher wants to know if the proportion of patients responding to a new drug is different from the proportion responding to the standard drug. Which hypothesis should be tested?

Accepted Answer

$$H_0$$: p_{new} = p_{standard}$$

Question 12

Which of the following is a reason to use a chi-square test for association rather than a two-proportion z-test?

Accepted Answer

When there are more than two categories for each variable.

Question 13

If the p-value for a test is 0.04 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following best describes the null hypothesis in a chi-square test for independence?

Accepted Answer

There is no association between the two categorical variables.

Question 15

A researcher finds a chi-square test statistic of 8.5 with 3 degrees of freedom. The critical value at the 0.05 significance level is 7.81. What should the researcher conclude?

Accepted Answer

Reject the null hypothesis; there is evidence of association.

Question 16

Which of the following is a valid interpretation of a p-value in hypothesis testing?

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 17

In a two-proportion z-test, which formula is used to calculate the pooled proportion?

Accepted Answer

$$\hat{p} = \frac{x_1$ + x_2$}{n_1$ + n_2$}$$

Question 18

A scientist is comparing the effectiveness of two fertilizers on plant growth. If the sample sizes are large and the proportions of plants that grew are 0.6 and 0.7, which test should be used to determine if the difference is significant?

Accepted Answer

Two-proportion z-test

Question 19

Which of the following is NOT a step in conducting a chi-square test for independence?

Accepted Answer

Calculate the mean and standard deviation of the data.

Study Notes: Associations between Categorical Variables (Chapter 10)

Guida di studio - Domande di pratica

Study guide - Flashcard