Question 1

A company claims that the average delivery time for its packages is 2 days. A random sample of 36 deliveries yields a sample mean of 2.3 days and a sample standard deviation of 0.6 days. Which of the following is the correct formula to calculate the 95% confidence interval for the population mean delivery time?

Accepted Answer

$$ \bar{x} \pm z_{\alpha/2} \cdot \frac{s}{\sqrt{n}} $$

Question 2

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

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 3

A pharmaceutical company wants to estimate the mean recovery time for a new drug. They want the margin of error to be no more than 1 day at a 95% confidence level. If the population standard deviation is estimated to be 4 days, what is the minimum sample size required?

Accepted Answer

$$ n = \left( \frac{z_{\alpha/2} \cdot \sigma}{E} \$$right)^2$$ $$

Question 4

A business analyst is testing whether the mean sales per day has changed from last year’s average of $$500. She sets up the following hypotheses: H_0$: \mu = 500$$, $$H_a: \mu 
eq 500$. What type of test is this?

Accepted Answer

Two-tailed test

Question 5

Suppose the p-value for a hypothesis test is 0.03 and the significance level $$\alpha is 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 6

A point estimator is best described as:

Accepted Answer

A single value calculated from sample data used to estimate a population parameter

Question 7

A manufacturer claims that less than 5% of its products are defective. To test this, a quality control manager samples 200 products and finds 12 defective items. Which of the following is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$ H_0$: p = 0.05, \quad H_a: p \u003c 0.05 $$

Question 8

Which of the following statements about confidence intervals is correct?

Accepted Answer

A 95% confidence interval means that if we repeated the sampling process many times, about 95% of the intervals would contain the true population parameter.

Question 9

A researcher is interested in the average number of hours students study per week. She collects a sample and wants to test if the average is greater than 15 hours. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$ H_a: \mu \u003e 15 $$

Question 10

In a hypothesis test, which of the following best describes the p-value?

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis

Question 11

A hospital administrator wants to know if the average wait time in the emergency room has increased from the previous mean of 30 minutes. She collects a sample and finds a mean wait time of 34 minutes with a standard deviation of 8 minutes and a sample size of 25. What is the value of the test statistic for testing $$H_0$$: \mu = 30$$?

Accepted Answer

$$ z = \frac{\bar{x} - \mu_0$}{s/\sqrt{n}} = \frac{34 - 30}{8/\sqrt{25}} $$

Question 12

Which of the following is an example of a reverse probability distribution problem?

Accepted Answer

Given a probability, find the value of $$x$$ that corresponds to it

Question 13

A Type II error occurs when:

Accepted Answer

We fail to reject the null hypothesis when it is actually false

Question 14

A company wants to test if a new training program increases employee productivity. The null hypothesis is $$H_0$$: \mu = 100$$ units per day. The sample mean is 105, the sample standard deviation is 10, and the sample size is 16. What is the calculated test statistic?

Accepted Answer

$$ z = \frac{105 - 100}{10/\sqrt{16}} = 2 $$

Question 15

Which of the following is NOT a step in the formal process of hypothesis testing?

Accepted Answer

Accepting the null hypothesis if the p-value is large

Question 16

A sample of 50 students has a mean test score of 78 with a standard deviation of 10. What is the 99% confidence interval for the population mean? (Use $$z_{\alpha/2} = 2.576)$$

Accepted Answer

$$ 78 \pm 2.576 \cdot \frac{10}{\sqrt{50}} $$

Question 17

In the context of business statistics, which of the following best describes the logic of hypothesis testing?

Accepted Answer

Assume the null hypothesis is true and use sample data to determine if there is enough evidence to reject it

Question 18

A market researcher wants to determine if the proportion of customers who prefer a new product is different from 0.5. Which of the following is the correct set of hypotheses?

Accepted Answer

$$ H_0$: p = 0.5, \quad H_a: p 
eq 0.5 $$

Question 19

Which of the following best describes a sampling distribution?

Accepted Answer

The probability distribution of a statistic based on all possible samples of a given size from a population

Probability Distributions, Estimation, and Hypothesis Testing: Core Concepts in Business Statistics

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