Q: If $$\sigma = 6.783$$ and you want a 90% confidence interval with a margin of error of 1, what sample size $$n$$ should you select?

$$ n = \left( \frac{z_{0.05} \times 6.783}{1} \$$right)^2$$ $$ where $$z_{0.05} = 1.645$$, so $$n = \left( \frac{1.645 \times 6.783}{1} \$$right)^2$$ = 124.$$

Question 1

A fitness trainer measures the body fat percentage of 12 clients before and after an 8-week workout program. The paired t-test yields a one-tailed p-value of 0.049 and a t-statistic of 1.81. At $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; the program is effective at reducing body fat percentage.

Question 2

A group of 10 students took a statistics exam before and after a tutoring session. The mean difference in scores was 6.4, with a standard deviation of 4.2. At $$\alpha = 0.05$$, what is the test statistic for the paired t-test?

Accepted Answer

$$ t = \frac{6.4}{4.2 / \sqrt{10}} = 4.83 $$

Question 3

A restaurant manager believes the average dinner check per customer is $$28. The population standard deviation is 6. A $$sample of 49 customers has an average check of $30.10. At the 10% significance level, what is the z-score for this test?

Accepted Answer

$$ z = \frac{30.10 - 28}{6 / \sqrt{49}} = 2.45 $$

Question 4

If $$\bar{x} = 75$$, sample standard deviation $$s = 11$$, $$n = 60$$, and $$\alpha = 0.10 in a $$one-sample hypothesis test where we reject the null hypothesis, what is the probability that we rejected the null when the null was actually true?

Accepted Answer

0.10

Question 5

All else equal, is it harder to reject the null hypothesis in a two-tailed test or a one-tailed test?

Accepted Answer

Two-tailed test

Question 6

If $$\sigma = 6.783$$ and you want a 90% confidence interval with a margin of error of 1, what sample size $$n$$ should you select?

Accepted Answer

$$ n = \left( \frac{z_{0.05} 	imes 6.783}{1} \$$right)^2$$ $$ where $$z_{0.05} = 1.645$$, so $$n = \left( \frac{1.645 	imes 6.783}{1} \$$right)^2$$ = 124.$$

Question 7

How does increasing the confidence level affect the width of a confidence interval, all else equal?

Accepted Answer

The width increases as the confidence level increases.

Question 8

What is the equation for coefficient of variation and what does it measure?

Accepted Answer

$$ CV = \frac{s}{\bar{x}} $$; it measures relative variability.

Question 9

Given the sample: 3, 7, 22, 16, 11, 9, 4, 31, 14, what is the sample standard deviation $$s$$?

Accepted Answer

$$ s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}} = 9.13 $$

Question 10

Are SAT scores categorical data?

Accepted Answer

No, SAT scores are quantitative (numerical) data.

Question 11

Given $$x = 11,9,13,15,12,8,16,12$$ and $$y = 13,15,17,19,22,26,28,16$$, what is the regression equation $$y = a + bx$$?

Accepted Answer

$$ y = 2.13 + 1.47x $$

Question 12

What is the correlation coefficient $$r$$ for $$x: 7,7,7,8,9,10,11$$ and $$y: 10,10,12,13,14,15,16$$?

Accepted Answer

$$ r = 0.97 $$

Question 13

The mean time to complete an exam is 2.5 hours, with a standard deviation of 0.5 hours. For a sample of 33 students, what is the probability that the sample mean is more than 2.62 hours?

Accepted Answer

$$ P(\bar{x} \u003e 2.62) = P\left(z \u003e \frac{2.62 - 2.5}{0.5 / \sqrt{33}}\right) = P(z \u003e 2.16) = 0.015 $$

Question 14

Assume credit scores are normally distributed with $$\mu = 715$$ and $$\sigma = 75. $$What is the probability that a random sample of 38 people has a mean credit score between 690 and 720?

Accepted Answer

$$ P(690 \u003c \bar{x} \u003c 720) = P\left(\frac{690 - 715}{75 / \sqrt{38}} \u003c z \u003c \frac{720 - 715}{75 / \sqrt{38}}\right) = P(-2.02 \u003c z \u003c 0.41) = 0.659 $$

Question 15

What happens to t-scores as sample size increases?

Accepted Answer

T-scores approach z-scores as sample size increases.

Question 16

The fuel efficiency of cars is normally distributed with a known standard deviation of 3 mpg. A sample of 20 cars has an average fuel efficiency of 25 mpg. What is the 90% confidence interval for the mean?

Accepted Answer

$$ 25 \pm 1.645 	imes \frac{3}{\sqrt{20}} = 25 \pm 1.10 $$

Question 17

What type of data are histograms used to illustrate?

Accepted Answer

Quantitative (numerical) data

Question 18

What level of measurement is a Likert scale?

Accepted Answer

Ordinal

Statistics for Business Exam 1 Review – Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards