Q: A university reports that 8.3% of students are members of a fraternity or sorority. If a random sample of 75 students is taken, what is the standard deviation of the number of fraternity/sorority members in the sample?

$$\sqrt{75 \times 0.083 \times (1 - 0.083)}$$

Q: IQ scores are normally distributed with a population standard deviation of 15. A sample of 144 students has a mean IQ score of 101.83. What is the 95% confidence interval for the population mean IQ score?

$$101.83 \pm 1.96 \times \frac{15}{\sqrt{144}}$$

Q: A random sample of 250 UMD students found that 167 indicated they live off campus. What is the 95% confidence interval for the population proportion of UMD students who live off campus?

$$\hat{p} \pm 1.96 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{250}}$$

Question 1

Which of the following variables from a student data file is quantitative?

Accepted Answer

Student's final exam score

Question 2

A histogram of restaurant bill amounts shows a distribution that is skewed right. Which of the following statements is most likely true?

Accepted Answer

The mean is greater than the median.

Question 3

For all U.S. students who take the ACT, scores are normally distributed with a mean of 21 and a standard deviation of 5. What percent of students have scores above 26? Use the Empirical Rule.

Accepted Answer

About 16%

Question 4

A carnival game involves rolling a fair six-sided die and spinning a spinner with three equally likely outcomes (X, Y, Z). What is the probability of getting a total score of 7 if the score is the sum of the die and spinner values (where X=1, Y=2, Z=3)?

Accepted Answer

$$\frac{3}{18}$$

Question 5

Given a discrete random variable $$X$$ with probability distribution $$P(X = x) = \frac{10 - x}{31}$$ for $$x = 3, 5, 7, 9$$, what is the mean of $$X$$?

Accepted Answer

$$5.81$$

Question 6

A university reports that 8.3% of students are members of a fraternity or sorority. If a random sample of 75 students is taken, what is the standard deviation of the number of fraternity/sorority members in the sample?

Accepted Answer

$$\sqrt{75 	imes 0.083 	imes (1 - 0.083)}$$

Question 7

For a particular scratch-off lottery ticket, the probability of winning $$10 is 0.025$. What is the probability of winning at least 10$$?

Accepted Answer

$$0.025$$

Question 8

Given Q1 = 79 and Q3 = 94 for a calculus exam, what is the interquartile range (IQR)?

Accepted Answer

$$15$$

Question 9

Using the 1.5*IQR criterion for outliers, what is the lower fence for the calculus exam scores if Q1 = 79 and IQR = 15?

Accepted Answer

$$79 - 1.5 	imes 15$$

Question 10

For all U.S. students who take the ACT, scores are normally distributed with a mean of 24.34 and a standard deviation of 5.62. What proportion of students have ACT scores above 31? Use the Z-table.

Accepted Answer

$$P(Z \u003e \frac{31 - 24.34}{5.62})$$

Question 11

A random sample of 225 U.S. college students found that 31 indicated they had a chronic digestive system condition. What is the sample proportion?

Accepted Answer

$$\frac{31}{225}$$

Question 12

IQ scores are normally distributed with a population standard deviation of 15. A sample of 144 students has a mean IQ score of 101.83. What is the 95% confidence interval for the population mean IQ score?

Accepted Answer

$$101.83 \pm 1.96 	imes \frac{15}{\sqrt{144}}$$

Question 13

A random sample of 250 UMD students found that 167 indicated they live off campus. What is the 95% confidence interval for the population proportion of UMD students who live off campus?

Accepted Answer

$$\hat{p} \pm 1.96 	imes \sqrt{\frac{\hat{p}(1-\hat{p})}{250}}$$

Question 14

Eden and Illa collected data from different samples of 100 UMD students and compared their mean SAT-Math scores. Eden's sample had a mean of 546 and Illa's sample had a mean of 563. If both samples have a standard deviation of 100, what is the test statistic for comparing the means?

Accepted Answer

$$\frac{546 - 563}{\sqrt{\frac{100^2$}{100} + \frac{100^2$}{100}}}$$

Question 15

You are performing a hypothesis test with $$H_1$$: \mu 
eq 275$$ and a test statistic of z = 1.57$. What is the p-value for this test?

Accepted Answer

$$2 	imes P(Z \u003e 1.57)$$

Question 16

Suppose the p-value of a hypothesis test is 0.0279. Which of the following is correct regarding the conclusions we can draw?

Accepted Answer

We can reject the null hypothesis at a significance level of $$\alpha = 0.05$$ but cannot reject at $$\alpha = 0.01.$$

Question 17

A study examined mathematics quiz scores in elementary students. Program 1 had a mean score of 21.85 (SD = 2.75, n = 50) and Program 2 had a mean score of 22.88 (SD = 2.50, n = 50). What is the test statistic for comparing the means?

Accepted Answer

$$\frac{21.85 - 22.88}{\sqrt{\frac{2.75^2$}{50} + \frac{2.50^2$}{50}}}$$

STAT100 Final Exam Study Guide: Key Concepts and Applications

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