Q: In a chi-square test of independence with 3 rows and 3 columns, what are the degrees of freedom?

$$df = (3-1) \times (3-1) = 4$$

Q: Which formula is used to calculate the expected frequency in a chi-square test of independence?

$$E_{ij} = \frac{(\text{row total}) \times (\text{column total})}{\text{grand total}}$$

Question 1

Which of the following best describes the purpose of the chi-square goodness of fit test?

Accepted Answer

To test whether the frequency distribution of a categorical variable is different from your expectations.

Question 2

A school administrator wants to know if students' favorite subjects are associated with their grade levels. Which statistical test should be used?

Accepted Answer

Chi-square test of independence

Question 3

Given a sample mean $$\bar{x} = 66$$, population mean $$\mu = 65$$, population standard deviation $$\sigma = 3$$, and sample size $$n = 50$$, what is the correct formula to calculate the z-test statistic?

Accepted Answer

$$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$

Question 4

A marketing team surveys 1,000 people and finds that 630 remember an ad. They want to test if more than 60% remember the ad. What is the null hypothesis ($$H_0$$)?

Accepted Answer

$$H_0$$: p \leq 0.60$$

Question 5

In a chi-square test of independence with 3 rows and 3 columns, what are the degrees of freedom?

Accepted Answer

$$df = (3-1) 	imes (3-1) = 4$$

Question 6

A wildlife biologist finds a sample mean weight of 68 kg for deer, with a historical mean of 70 kg, $$\sigma = 8$$, and $$n = 25. $$What is the calculated z-score?

Accepted Answer

$$z = \frac{68 - 70}{8 / \sqrt{25}} = -1.25$$

Question 7

Which of the following is the correct decision rule for a left-tailed z-test at $$\alpha = 0.05$$?

Accepted Answer

Reject $$H_0 if$$ $$Z_{calc} \u003c -1.645$$

Question 8

Which formula is used to calculate the expected frequency in a chi-square test of independence?

Accepted Answer

$$E_{ij} = \frac{(	ext{row total}) 	imes (	ext{column total})}{	ext{grand total}}$$

Question 9

If the calculated chi-square statistic is 18.332 and the critical value at $$\alpha = 0.05$$ with 4 degrees of freedom is 9.488, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is an association between the variables.

Question 10

Which of the following is NOT an assumption for using the one-sample z-test for a mean?

Accepted Answer

The population standard deviation is unknown.

Question 11

A coin is tossed 20 times. What is the probability of getting exactly 15 heads, assuming the coin is fair? Which distribution should be used?

Accepted Answer

Binomial distribution

Question 12

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

Accepted Answer

$$T = \frac{X - np}{\sqrt{np(1-p)}}$$

Question 13

A sample of 25 garlic packs has a mean weight of 499g, with a known population standard deviation of 10g. The label claims 500g. What is the null hypothesis?

Accepted Answer

$$H_0$$: \mu = 500$$

Question 14

In a two-tailed z-test at $$\alpha = 0.05$$, what is the rejection region?

Accepted Answer

Reject $$H_0 if$$ $$Z  1.96$$

Question 15

Which of the following best describes the alternative hypothesis in a right-tailed one-sample z-test for a mean?

Accepted Answer

$$H_1$$: \mu \u003e \$$mu_0$$

Question 16

A calculated z-score is -0.12 for a left-tailed test with $$z_{crit} = -1.645. $$What is the correct conclusion?

Accepted Answer

Do not reject the null hypothesis.

Chi-Square Tests and One-Sample Z-Tests: Hypothesis Testing in Statistics

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