Math 227 Fall 2015 Practice Final

#1 True/False

______(a) The standard deviation, s, is not effected by extreme data.

______(b) If the population distribution is not normally distributed,

the distribution for the sampling mean will be approximately

normally distributed for n = 20.

______(c) 5/3 cannot be an answer for a probability.

______(d) On a five possible answers multiple-choice question, the

probability of answering the question correctly by random

guessing is 1/2.

______(f) The claim is always the same as Ho.

#2 A card is selected randomly from a deck of cards, what is the probability that a face

card (Jack, Queen, King) or a club will be selected.

#3 Two dice are tossed. What is the probability of getting a sum of 8?

#4 A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure, measured in mm HG, by following a particular diet. Use a significance level of 0.01 to test the claim that the treatment group is from a population with a smaller mean than the control group.

Treatment Group Control Group

#5 Listed below are the Titanic mortality data.

Men Women Boys Girls

Survived 332 318 29 27

Died 1360 104 35 18

(a) If we randomly select someone who was aboard the Titanic, what is the

probability of getting a man or a person who survived?

(b) What is the probability of getting a woman, given the selected person died?

#6 (a) Find P(x = 3) for the following probability distribution table.

x 1 2 3 4

P(x) 0.12 0.21 ? 0.18

(b) Find the mean of the probability distribution.

#7 It was found that 55% of American victims of health care fraud are senior

citizens. If 20 victims are randomly selected,

(a) find the probability that exactly 14 are senior citizens.

(b) find m and s for this binomial distribution.

#8 The average amount of rain per year in Greenville is 49 inches. The standard

deviation is 8 inches. Find the probability that next year Greenville will receive

the amount of rainfall in between 46 and 54 inches.

#9 If the average score of a reading test is 122.6 with the standard deviation of 18, find

the cutoff-score for the bottom 5%. Assume the variable is normally distributed.

#10 The average annual salary in Pennsylvania was $24,393 in 1992. Assume that

salaries were normally distributed for a certain group of wage earners, and the

standard deviation of this group was $4362. Find the probability that, for a

randomly selected sample of 25 individuals, the mean salary was less than

$26,000.

#11 A researcher is interested in estimating the average monthly salary of sports reporters

in a large city. He wants to be 99% confident that his estimate is correct. If s = $1100,

how large a sample must be selected if he wishes to be accurate to within $150?

#12 A sample of 500 nursing applications included 60 from men. Find the 90% confidence

interval of the true proportion of men who applied to the nursing program.

#13 An attorney claims that more than 25% of all lawyers advertise. A sample of 200

lawyers in a certain city showed that 63 had used some form of advertising.

At a = 0.05, is there enough evidence to support the attorney’s claim?

#14 A state executive claims that the average number of acres in western Pennsylvania

state parks is less than 2000 acres. A random sample of five parks is selected, and

the number of acres is shown.

959 1187 493 6249 541

(a) Use your calculator to find the sample mean and the sample standard deviation.

(b) At a = 0.01, is there enough evidence to support the claim?

#15 Heights of men have a bell-shaped distribution with a mean of 176 cm and a standard deviation of 7

cm. Using the empirical rule, what is the approximate percentage of men between 155 cm and 197

cm?

#16 Jim gets test grades of 79, 75, 82, and 85. He gets a 94 on his final exam. Find the weighted mean if the tests each count for 10% and the final exam counts for 60% the final grade.

#17 If Z is a standard normal variable, find the probability that Z is greater than -2.89.

#18 Determine whether the given procedure results in a binomial distribution. Why or why not?

Toss a coin 25 times, keeping track of the number of tails.

#19 A data set includes a simple random sample of 37 weights of post-1983 pennies. Those 37 weights have a mean of 2.49910 g and a standard deviation of 0.01648 g. U.S. Mint specifications require that pennies be manufactures so that the mean weight is 2.500 g. Use a 0.05 significance level to test the claim that the population of weights has a standard deviation less than the specification of 0.0230 g.

#20 For the following data: 14 15 8 11 8 8 9 1 12 8 7 15

(a) Find the Mean

(b) Find the Median

(c) Find the Mode

(d) Find the Five-number summary (Low, Q1, Q2, Q3, High)

(e) Construct a boxplot

#21 Find the z value to the left of the mean so that 60.64% of the area under the distribution

curve lies to the right of it.

#22 Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are

normally distributed with a standard deviation of $1500, find the probability that the student

makes between $13,000 and $14000.

#23 Given the equation of the regression line and the correlation

coefficient , find the best predicted value of y for x = 2.00. What is r?

#24 State the four requirements for a Binomial Experiment.

#25 Find the p-value for a right tailed test with observed

#26 One survey showed that among 785 randomly selected subjects who completed four

years of college, 144 smoke. Use to test the claim that the percentage (p) of

smoking among those with four years of college is less than the 27% rate for the general

population.

#27 The mean is and the standard deviation is , find the probability that X is between 135.0 an d143.2. X has a normal distribution

#28 What is Type I and Type II errors?

#29 A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage. Construct a 99% confidence interval for the proportion of adult
Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage. Interpret the results.

#30 Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities?

Lemon imports / 230 / 265 / 358 / 480 / 530
Crash Fatality Rate / 15.9 / 15.7 / 15.4 / 15.3 / 14.9

Conduct a formal hypothesis test of the claim that there is a linear correlation between

the two variables.

#31 A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.

College A / College B / College C / College D
Smoke / 17 / 26 / 11 / 34
Don’t smoke / 83 / 74 / 89 / 66

Use a 0.01 significance level to test the claim that the proportion of students smoking is the

same at all four colleges.

#32 The following table shows the number of employees who called in sick at a business for different days of a particular week.

Day / Sun / Mon / Tues / Wed / Thurs / Fri / Sat
Number sick / 8 / 12 / 7 / 11 / 9 / 11 / 12

a)  At the 0.05 level of significance, test the claim that sick days occur with equal frequency on the different days of the week

b)  Test the claim after changing the frequency for Saturday to 152. Describe the effect of this outlier on the test.

#33 Use a test to test the claim that in the given contingency table, the row variable and the column variable are independent.

60 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent.

Correct / Incorrect
Math / 27 / 53
English / 43 / 37