Q: A hospital administrator wants to know if the average wait time in the emergency room has changed from last year’s average of 45 minutes. Which is the correct set of hypotheses for a two-tailed test?

$$ H_0$: \mu = 45,\ H_1$: \mu \neq 45 $$

Question 1

A business analyst wants to compare the average sales between two independent retail stores. Which statistical test is most appropriate for this scenario?

Accepted Answer

Two-sample t-test

Question 2

A company claims that their new process reduces the average production time from 50 minutes. A random sample of 30 production times yields a sample mean of 48 minutes and a standard deviation of 5 minutes. Which formula should be used to calculate the test statistic for this hypothesis test?

Accepted Answer

$$ t = \frac{\bar{x} - \mu_0$}{s / \sqrt{n}} $$

Question 3

Which of the following is an assumption of the one-way ANOVA test?

Accepted Answer

The populations have equal variances

Question 4

A pharmaceutical company wants to test if a new drug has a different effect than the current standard. Which is the correct null hypothesis for a two-tailed test comparing means?

Accepted Answer

$$ H_0$: \mu_{new} = \mu_{standard} $$

Question 5

A manager wants to know if the proportion of defective products has changed from the historical rate of 5%. In a sample of 200 products, 16 are defective. What is the value of the sample proportion?

Accepted Answer

$$ \frac{16}{200} = 0.08 $$

Question 6

Which of the following best describes a Type II error in hypothesis testing?

Accepted Answer

Failing to reject a false null hypothesis

Question 7

A marketing team wants to test if the average time spent on their website is greater than 3 minutes. Which is the correct alternative hypothesis?

Accepted Answer

$$ H_1$: \mu \u003e 3 $$

Question 8

A researcher is comparing the mean test scores of students before and after a training program using the same group of students. Which test should be used?

Accepted Answer

Paired t-test

Question 9

If the p-value for a hypothesis test is 0.03 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 10

A business wants to estimate the mean monthly spending of its customers with 95% confidence. Which formula gives the margin of error for the confidence interval when the population standard deviation is unknown?

Accepted Answer

$$ E = t^* \frac{s}{\sqrt{n}} $$

Question 11

A company is testing whether the mean weight of their product is different from 500g. They collect a sample and calculate a 95% confidence interval for the mean as (495g, 505g). What does this interval suggest?

Accepted Answer

There is not enough evidence to conclude the mean is different from 500g

Question 12

Which of the following is NOT a requirement for using the Central Limit Theorem to approximate the sampling distribution of the sample mean?

Accepted Answer

The population distribution must be normal for any sample size

Question 13

A hospital administrator wants to know if the average wait time in the emergency room has changed from last year’s average of 45 minutes. Which is the correct set of hypotheses for a two-tailed test?

Accepted Answer

$$ H_0$: \mu = 45,\ H_1$: \mu 
eq 45 $$

Question 14

A researcher is testing the effectiveness of four different diets on weight loss. Which statistical method should be used to determine if there is a significant difference among the diets?

Accepted Answer

One-way ANOVA

Question 15

A business wants to test if the proportion of customers who prefer a new product is greater than 0.5. Which is the correct alternative hypothesis?

Accepted Answer

$$ H_1$: p \u003e 0.5 $$

Question 16

A sample of 40 students has a mean test score of 78 and a standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$ \frac{10}{\sqrt{40}} = 1.58 $$

Question 17

A company wants to compare the mean productivity of three different departments. Which test should be used?

Accepted Answer

One-way ANOVA

Question 18

Which of the following statements about p-values is TRUE?

Accepted Answer

A small p-value indicates strong evidence against the null hypothesis

Question 19

A manufacturer claims that less than 2% of their products are defective. In a random sample of 500 products, 15 are found to be defective. What is the sample proportion of defective products?

Accepted Answer

$$ \frac{15}{500} = 0.03 $$

Question 20

A business wants to test if the mean delivery time is less than 24 hours. Which is the correct null hypothesis?

Accepted Answer

$$ H_0$: \mu \geq 24 $$

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