Q: A researcher collects a sample of 36 transistors with a mean lifetime of 1210 hours and a sample standard deviation of 92 hours. What is the 95% confidence interval for the mean transistor lifetime?

$$1210 \pm t \times \frac{92}{\sqrt{36}}$$

Q: In a two-way table, what is the formula for the expected frequency for a cell?

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

Question 1

Which formula is used to calculate the t statistic for a sample mean when the population standard deviation is unknown?

Accepted Answer

$$t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$$

Question 2

A researcher collects a sample of 36 transistors with a mean lifetime of 1210 hours and a sample standard deviation of 92 hours. What is the 95% confidence interval for the mean transistor lifetime?

Accepted Answer

$$1210 \pm t 	imes \frac{92}{\sqrt{36}}$$

Question 3

Which property of the t distribution is true as the degrees of freedom increase?

Accepted Answer

The t distribution approaches the standard normal distribution.

Question 4

When performing a two-tailed t-test, when do you reject the null hypothesis?

Accepted Answer

If the test statistic is greater than or equal to the critical value or less than or equal to the negative of the critical value.

Question 5

A soft-drink vending machine is set to dispense 6 oz per cup. A sample of 30 cups yields a mean of 5.9 oz and a standard deviation of 0.25 oz. What is the correct test statistic to use for testing if the machine is underfilling?

Accepted Answer

$$t = \frac{5.9 - 6}{0.25 / \sqrt{30}}$$

Question 6

Which Excel function would you use to find the critical value for a two-tailed t-test with 20 degrees of freedom at the 0.05 significance level?

Accepted Answer

=T.INV.2T(0.05, 20)

Question 7

In a two-way table, what is the formula for the expected frequency for a cell?

Accepted Answer

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

Question 8

Which formula is used to calculate the chi-square statistic for a two-way table?

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O - E)^2$}{E}$$

Question 9

A sample of 255 undergraduates is classified by gender and college. What is the probability that a randomly selected student is a female in the College of Engineering (COE), given there are 30 such students?

Accepted Answer

$$\frac{30}{255}$$

Question 10

Which of the following is the correct null hypothesis for a chi-square test of independence in a two-way table?

Accepted Answer

$$H_0$$: The row and column variables are independent.

Question 11

Given the following data from a study of high school students: 731 tested while driving and drank alcohol, 3054 did not drink alcohol but tested while driving, 146 did not test while driving but drank alcohol, and 4564 did not test or drink. What is the probability that a student tested while driving?

Accepted Answer

$$\frac{731 + 3054}{731 + 3054 + 146 + 4564}$$

Question 12

If you want to test whether texting while driving is independent of drinking while driving at the 0.05 significance level, which test should you use?

Accepted Answer

Chi-square test of independence

Question 13

What is the formula for the confidence interval for a mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} - E \u003c \mu \u003c \bar{x} + E$$

Question 14

Which Excel function would you use to find the critical value for a chi-square test with 2 degrees of freedom at the 0.05 significance level?

Accepted Answer

=CHISQ.INV(0.95, 2)

Question 15

A sample of 12 rainstorms yields pH values: 6.1, 5.4, 4.8, 5.8, 6.6, 5.3, 6.1, 4.1, 3.9, 6.8, 6.5, 5.3. The historical mean is 5.2. What is the correct null hypothesis for testing if the mean pH has changed?

Accepted Answer

$$H_0$$: \mu = 5.2$$

Question 16

When calculating the degrees of freedom for a t-test for a single mean, which formula should you use?

Accepted Answer

$$df = n - 1$$

Question 17

Which of the following best describes a two-way table?

Accepted Answer

A table that shows the relationship between two variables by listing one variable in rows and the other in columns.

Question 18

If the calculated $$\$$chi^2$$ statistic is less than the critical value, what is the correct conclusion for a chi-square test of independence?

Accepted Answer

Do not reject the null hypothesis; the variables are independent.

t Tests and Two-Way Tables: Inference for Means and Categorical Data

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