Q: A business wants to estimate the average amount spent by customers in its store. A random sample of 64 customers has a mean of $$80 and a standard deviation of 16. $$What is the 95% confidence interval for the mean amount spent? (Use $$z^* = 1.96)$$

$$ 80 \pm 1.96 \times \frac{16}{8} = 80 \pm 3.92 $$

Question 1

A company wants to test whether the average time to assemble a product has changed from the historical mean of 30 minutes. Which statistical test is most appropriate for this scenario?

Accepted Answer

A one-sample t-test for the mean

Question 2

Which of the following is the correct formula for a 95% confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$ \bar{x} \pm t^* \frac{s}{\sqrt{n}} $$

Question 3

A business analyst is comparing the mean sales of two different stores. Which hypothesis test should be used if the population variances are unknown but assumed equal?

Accepted Answer

Two-sample t-test with pooled variance

Question 4

Which of the following statements about the p-value is correct?

Accepted Answer

The p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 5

A manufacturer claims that less than 5% of its products are defective. In a random sample of 200 products, 12 are found to be defective. What is the sample proportion of defective products?

Accepted Answer

$$ \frac{12}{200} = 0.06 $$

Question 6

Which of the following is the correct null hypothesis for testing whether the mean salary of employees at a company is $50,000?

Accepted Answer

$$ H_0$: \mu = 50,000 $$

Question 7

A researcher wants to compare the effectiveness of three different marketing strategies on sales. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Question 8

Which formula represents the test statistic for a one-sample z-test for a population mean when the population standard deviation is known?

Accepted Answer

$$ z = \frac{\bar{x} - \mu_0$}{\sigma / \sqrt{n}} $$

Question 9

A company wants to know if there is a relationship between gender (male/female) and department (sales/marketing/finance) among its employees. Which test should be used?

Accepted Answer

Chi-square test for independence

Question 10

Which of the following is an assumption of the standard normal distribution?

Accepted Answer

The mean is 0 and the standard deviation is 1.

Question 11

A business wants to estimate the average amount spent by customers in its store. A random sample of 64 customers has a mean of $$80 and a standard deviation of 16. $$What is the 95% confidence interval for the mean amount spent? (Use $$z^* = 1.96)$$

Accepted Answer

$$ 80 \pm 1.96 	imes \frac{16}{8} = 80 \pm 3.92 $$

Question 12

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

Accepted Answer

To make inferences about a population based on sample data

Question 13

A company is interested in whether the proportion of customers who prefer online shopping is different from 0.5. Which is the correct alternative hypothesis?

Accepted Answer

$$ H_a: p 
eq 0.5 $$

Question 14

Which of the following is the correct formula for the test statistic in a chi-square test for independence?

Accepted Answer

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

Question 15

A regression analysis yields the equation $$ \hat{y} = 2 + 3x . $$What is the predicted value of $$ y $$ when $$ x = 4 $$?

Accepted Answer

$$ 14 $$

Question 16

Which of the following is NOT an assumption of the least squares regression model?

Accepted Answer

The errors are correlated with the independent variable.

Question 17

A business wants to test if the mean number of customer complaints per month has decreased after implementing a new policy. Which type of hypothesis test is most appropriate?

Accepted Answer

A one-tailed (left) t-test for the mean

Question 18

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

Accepted Answer

Rejecting a true null hypothesis

Question 19

A company is comparing the variances of two production processes. Which test should be used?

Accepted Answer

F-test for equality of variances

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