Q: A researcher wants to test if the average commute time in a city is different from 30 minutes. A random sample of 25 commuters has a mean of 32 minutes and a standard deviation of 6 minutes. What are the null and alternative hypotheses for this two-tailed test?

$$ H_0$: \mu = 30, \quad H_a: \mu \neq 30 $$

Question 1

Which of the following is the correct formula for the t-test statistic when the population standard deviation is unknown?

Accepted Answer

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

Question 2

A researcher wants to test if the average commute time in a city is different from 30 minutes. A random sample of 25 commuters has a mean of 32 minutes and a standard deviation of 6 minutes. What are the null and alternative hypotheses for this two-tailed test?

Accepted Answer

$$ H_0$: \mu = 30, \quad H_a: \mu 
eq 30 $$

Question 3

When conducting a left-tailed t-test with a significance level of $$ \alpha = 0.05 $$ and a sample size of 16, what is the degrees of freedom used to find the critical value?

Accepted Answer

$$ df = 15 $$

Question 4

A used car dealer claims the mean price of cars sold is at least $$29,100. A sample of 14 cars has a mean price of 27$$,177 and a standard deviation of $3,250. Which of the following is the correct alternative hypothesis to test the dealer’s claim?

Accepted Answer

$$ H_a: \mu \u003c 29,100 $$

Question 5

Which of the following conditions must be met to use the t-test for a mean when $$ \sigma  is $$unknown?

Accepted Answer

The sample is random and the population is normally distributed or $$ n \geq 30 $$

Question 6

If a hypothesis test has a significance level of $$ \alpha = 0.01 $$ and the calculated P-value is 0.03, what is the correct decision?

Accepted Answer

Fail to reject the null hypothesis

Question 7

A company claims the mean pH of river water is 6.8. A sample of 39 measurements yields a mean of 6.7 and a standard deviation of 0.35. What is the test statistic for this hypothesis test?

Accepted Answer

$$ t = \frac{6.7 - 6.8}{\frac{0.35}{\sqrt{39}}} $$

Question 8

Which of the following best describes the rejection region for a right-tailed t-test at $$ \alpha = 0.05 $$?

Accepted Answer

$$ t \u003e t_{\alpha, df} $$

Question 9

A department of motor vehicles claims the mean wait time is less than 14 minutes. A sample of 10 people has a mean wait time of 13 minutes and a standard deviation of 3.5 minutes. What is the correct null hypothesis?

Accepted Answer

$$ H_0$: \mu = 14 $$

Question 10

If the calculated t-statistic falls within the rejection region, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 11

Which of the following is NOT a step in finding the critical value for a t-distribution?

Accepted Answer

Calculate the sample variance

Question 12

A two-tailed t-test is being conducted at $$ \alpha = 0.05 $$ with 20 degrees of freedom. Which column in the t-table should be used to find the critical values?

Accepted Answer

Two Tails, $$ \alpha = 0.05 $$

Question 13

Which scenario best illustrates the use of a left-tailed t-test?

Accepted Answer

Testing if the mean salary is less than a claimed value

Question 14

If a sample mean is much lower than the claimed population mean and the test is left-tailed, what is likely to happen to the null hypothesis?

Accepted Answer

It will be rejected

Question 15

Which of the following best describes the P-value in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true

Hypothesis Testing for the Mean (Sigma Unknown) – t-Test Applications

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