Question 1

Which of the following best describes the primary purpose of hypothesis testing in business statistics?

Accepted Answer

To make data-driven decisions by evaluating evidence against a null hypothesis.

Question 2

A pharmaceutical company wants to test if a new drug is more effective than the current standard. Which is the most appropriate null hypothesis ($$H_0) $$for this scenario?

Accepted Answer

$$H_0$$: The new drug is equally effective as the current standard.

Question 3

Which formula is used to calculate the test statistic for a one-sample $$z-$$test when the population standard deviation is known?

Accepted Answer

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

Question 4

A company claims their customer satisfaction rate is 90%. You collect a random sample and find a satisfaction rate of 85%. Which statistical concept allows you to determine if this difference is significant?

Accepted Answer

Hypothesis testing

Question 5

Which of the following is a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 6

In a two-tailed hypothesis test, what does the $$p-$$value represent?

Accepted Answer

The probability of observing a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.

Question 7

A hospital wants to know if a new treatment reduces average recovery time. The sample mean recovery time is 5 days, population mean is 6 days, population standard deviation is 1.5 days, and sample size is 36. What is the $$z-$$score?

Accepted Answer

$$z = \frac{5 - 6}{1.5 / \sqrt{36}} = -4$$

Question 8

Which of the following is NOT an assumption for conducting a $$t-$$test?

Accepted Answer

The population standard deviation is known.

Question 9

A business analyst wants to test if the mean sales after a marketing campaign are different from the previous mean of $$\10$$,000$$. Which is the correct alternative hypothesis (H_a$)?

Accepted Answer

$$H_a: \mu 
eq 10,000$$

Question 10

If the significance level ($$\alpha) is $$set at 0.05, what does this mean in the context of hypothesis testing?

Accepted Answer

There is a 5% chance of rejecting the null hypothesis when it is true.

Question 11

A researcher is testing whether a coin is fair. She flips the coin 100 times and gets 60 heads. What is the null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: The probability of heads is 0.5.

Question 12

Which formula is used to calculate the $$t-$$statistic for a one-sample $$t-$$test?

Accepted Answer

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

Question 13

A company wants to know if a new training program increases employee productivity. Which statistical test should be used if the sample size is small and the population standard deviation is unknown?

Accepted Answer

One-sample $$t-$$test

Question 14

Which of the following best describes the alternative hypothesis ($$H_a) in $$hypothesis testing?

Accepted Answer

It is a statement that contradicts the null hypothesis.

Question 15

A medical researcher tests whether a new vaccine is more effective than the old one. She sets $$\alpha = 0.01. $$What does this mean?

Accepted Answer

She is willing to accept a 1% chance of making a Type I error.

Question 16

Which of the following scenarios best illustrates the use of probability in hypothesis testing?

Accepted Answer

Determining the likelihood of observing a sample mean given a population mean.

Question 17

A factory manager wants to test if the average weight of a product is less than the advertised weight of 500g. Which is the correct null hypothesis ($$H_0$$)?

Accepted Answer

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

Question 18

Which of the following is a real-world example of a one-tailed hypothesis test?

Accepted Answer

Testing if a new teaching method results in higher test scores than the traditional method.

Question 19

A researcher sets $$\alpha = 0.05$$ and obtains a $$p-$$value of 0.03. What should she conclude?

Accepted Answer

Reject the null hypothesis.

Course Syllabus: Analyzing Business Problems With Hypothesis Testing

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