MATH 2228 Statistics Final Exam Macleod

An economist wanted to estimate the mean expenditure on snacks at movie theaters in a certain city. A random sample of 25 moviegoers revealed a mean amount of $6.25 and a standard deviation in the sample of $0.75. Obtain a 95% confidence interval to estimate the mean amount spent on snacks at theaters in this city.

$5.94 < μ < $6.56

Which of the following correlation coefficients indicates the strongest linear relationship between two variables x and y?

-0.84

Which one of these p-values provides the strongest evidence against the null hypothesis (H0) in favor of the alternative hypothesis (Ha)?

.0001

Suppose the z-score for a test statistic in a two-tailed test is z = 2.14, what would be the p-value?

.0324

X = the number of automobiles requiring repairs Y = the number of automobiles not requiring repairs 30% of the automobiles inspected at a state inspection station required repairs to meet the inspection standard. Six drivers arrive for auto inspections. Find the probability that exactly two automobiles will require repair.

.3241

Find: P ( - 2.31 < Z < 0.14 ) using the standard normal distribution table.

.5453

Suppose the manager for a car dealership wants to know the proportion of white cars owned in his town. He sent one of his employees out and instructs him to take a sample of 150 cars and use that to build a 98% confidence interval to estimate the overall proportion. In the sample of 150 cars, there were 87 that were white. Help this employee to begin building the confidence interval.

.58 ± 2.326(σp̂)

Suppose the probability that an animal has sharp frippets is .35. In a sample of 12 animals, what is the probability that between 2 and 6 of them have sharp frippets? Use the Binomial tables provided or p. 117.

.6360

The ages of the runners in a 10K race normally distributed with a mean of 32 and a standard deviation of 9. What is the probability that a sample of 12 runners will have an average age of less than 35?

.8749

The ages of the runners in a 10K race normally distributed with a mean of 45 and a standard deviation of 7. What is the probability that a randomly chosen runner is older than 30?

.9838

If events A and B are mutually exclusive and P(A) = .6 and P(B) = .3, find P(B|A).

0

The lengths of cats' tails are normally distributed with a mean of 8.1 inches and a standard deviation of 1.4 inches. What is the probability that a cat's tail would be exactly 9 inches.

0

If events A and B are independent and P(A) = .4 and P(B) = .2, find P(A U B).

0.52

A football kicker makes 54 out of 60 after-touchdown kicks. What is the probability that the kicker makes his next after-touchdown kick?

0.90

A sample of 250 people were asked how many cups of coffee they drink in the morning. You are given the following sample information: Cups of Coffee Probability 0 .12 1 .25 2 .43 3 .20 The expected number of cups of coffee a person drinks in the morning is which of the following

1.71

The time for a child to complete a task is normally distributed with a mean of 56.7 minutes and a standard deviation of 7.4 minutes. To find the probability that a sample of 15 children would have a mean completion time of more than 60 minutes, what standard deviation would you use in your z-score calculation?

1.911

The Z-value for a 95% confidence interval estimation for μ is

1.960

A study was conducted to investigate the relationship between the number of miles driven by a family per week y and the number of children in the family x. From the data collected the equation of the least squares regression line was ŷ = 100 + 10x and the correlation coefficient was r = .8. What would be the estimated number of miles driven per week for a family with 2 children?

120

If it was determined that it was necessary to use degrees of freedom in a problem where there was a 98% level of confidence and that sample size was 12, what value would you use from the table?

2.718

What percent of the 80 people in this sample have Type A blood? blood type frequency A 16 B 24 O 32 AB 8

20%

The FIVE-NUMBER SUMMARY for a given set of test scores is: 34 58 77 83 97 What percent of the scores is between 83 and 97?

25%

A survey of college students taking the professional exam to be certified as public school teachers shows that 25 percent fail. On a national exam day, 12,000 students take the test. Let X denote the number of students who fail. Find the mean and standard deviation of this Binomial random variable X.

3000; 47.43

An automobile manufacturer wants to determine what proportion of its customers are dissatisfied with the service received from their local dealer. The manufacturer's manager feels the proportion of dissatisfied customer is no more than 10%. How many customers should they sample if they want to be correct to within 3% of the actual proportion with a 95% level of confidence?

385

Below is a sample of 6 weekly driving distances for a college student. 38 66 42 35 23 30 Find the mean and standard deviation.

39; 14.8

The ages of 20 people at a small party are given in the stem plot below. Use it to find the value for the 48th percentile (P48). 2| 6 7 3| 0 2 5 6 8 4| 1 1 3 4 6 8 9 5| 2 4 4 5 8 6| 0

43

If a person receives a grade that is better than 55% of the population taking a test, but lower than 45% of the population, his/her grade is said to be at which of the following?

55th percentile

Suppose the variance for a set of weights is 42.3 lbs2 . What is the standard deviation?

6.5 lbs

Suppose the weights of newborn babies is normally distributed with a mean of 7 lbs and a standard deviation of 1.5 pounds. How much would a baby have to weigh to be in the top 10% of birthweights?

8.92

Suppose we want to estimate the average amount spent on books by freshmen in their first year at a major university. We want to be 96% confident that our estimate will be within $8 of the actual mean. It has been determined from earlier studies that the amount spent has a standard deviation of $35. How many freshmen should be sampled?

81

Which ONE of the following sampling distributions is approximately normal?

p̂ distribution with p = .40 and sample of size 20

A study was conducted to investigate the relationship between the number of miles driven by a family per week y and the number of children in the family x. From the data collected the equation of the least squares regression line was ŷ = 100 + 10x and the correlation coefficient was r = .8. Which of the following would be the correct interpretation of the slope for this regression equation?

As the number of children in the family increases by 1, the distance driven per week increases by 10 miles.

In the following Binomial problem X = # of planes that are on time p = .70 Y = # of planes that are not on time q = .30 What would be the best Binomial method to use to find the probability that between 4 and 8 of the next 10 planes will be on time ?

Binomial tables

An experiment was conducted and the following things were done to ensure that the results would be valid. a large number of subjects was used to insure the reliability of the results neither the subjects nor the experimenter knew who received which treatment until the conclusion of the experiment the names of the subjects were placed in a box, mixed, and drawn in order to assign the subjects to their treatment group there was a group that did not receive the experimental treatment so that the results between the two groups could be compared Which list of requirements for a good experiment matches the order of things done given above?

replication, double blindness, randomization, control

Choose the correct string of words to fill in the blanks. The Central Limit Theorem guarantees that a ____________________ will be ______________ as long as the sample size is _______________ , regardless of the shape of the population.

sampling distribution, normal, large

A filling machine is supposed to be putting 12 ounces of soda into cans. There have been concerns that it is underfilling the cans. A sample of 200 cans is taken and the mean amount in the sample is 11.42 ounces. An hypothesis test is going to be conducted to see if the sample indicates that the mean amount is significantly less than 12 ounces. Which of the following would be the correct hypotheses for this test?

H0 : µ = 12 Ha : µ < 12

Larry's car averages 33 miles per gallon on the highway. He recently made some modifications to his car that he thinks may have decreased his gas mileage. After driving 3000 highway miles with the modifications, Larry estimates the new gas mileage to be 30 mpg. He wishes to test if the modifications significantly decreased his gas mileage. Which of the following is the appropriate null hypothesis?

Ho: μ = 33

The following distributions show the scores for two students on eight 10-point quizzes. student 1: 7 8 7 9 8 6 7 8 student 2: 5 7 10 4 1 3 8 0 Which student's scores have the larger standard deviation? (No calculation is required.)

student 2

It has been determined that 45% of all college students attend schools within 150 miles of their homes. So X = # of students who live within 150 miles of home Y = # of students who do not live within 150 miles of home In a sample of 50 college students is taken. Which of the following is a true statement about this distribution?

It is normal because np and nq are both greater than 5

The Brody School of Medicine at ECU conducted a survey over 900 residents of Greenville and found that 250 of the surveyed people worried about being able to pay their medical costs next year. The sample and the population of interest were, respectively,

the 900 people surveyed; all Greenville residents

Which of the following could never be described by a Binomial distribution?

the amount of water used daily by a single household

The FIVE-NUMBER SUMMARY for a given set of test scores is: 34 58 77 83 97 A score of 58 is which of the following?

Q1

Suppose the data in an hypothesis test leads a researcher to reject the null hypothesis H0. What should be concluded about the alternative hypothesis Ha?

The conjecture in Ha is supported

In essence, a trial-by-jury is an hypothesis test, where H0: a person is innocent Ha: a person is guilty Strong enough evidence has to be presented by the prosecution to prove to the jury that the accused person did indeed commit the crime. Suppose the jury is not convinced by the prosecution's evidence and delivers a not guilty verdict, and five years later it is determined that the person truly wasn't guilty of the crime. Which of the following is the case?

The jury did not reject H0; five years later it is shown that no error was committed

Two years ago, it was determined that 38% of young adults vaped on a regular basis. A researcher is wondering whether that proportion has changed. A broad sample of 1200 young adults is taken and 45% of them said that they vape regularly. An hypothesis test is conducted to determine whether or not this indicates a significant change in the proportion of young adults who vape. For this problem, suppose the test was conducted and the p-value turned out to be .0365, what would you conclude?

The proportion of young adults who vape is significantly different than what it was two years ago

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students. Suppose that the 95% confidence interval for the true proportion of students on financial aid is (.59 ± .07). Interpret this interval.

We are 95% confident that the percentage of all students at this university receiving financial aid falls between 52% and 66%.

In the following Binomial problem X = # of planes that are on time p = .80 Y = # of planes that are not on time q = .20 To find the probability that more than 42 of the next 60 planes will be on time, which of the following would be an appropriate calculation?

Z = 42.5 - 48 / 3.098

To show a cause/effect relationship between to variables, which of the following could be used?

a controlled experiment

Which of the following is a discrete distribution?

binomial

An ECU professor analyzed the data collected from a random sample 500 college students. One of his goals was to estimate the average number of books they have to buy per semester and their average commute distance to campus. The commute distance is an example of a _______ random variable and the number of books/semester is an example of a _______ random variable.

continuous, discrete

The sequence of steps taken when conducting an hypothesis test is:

formulate the null and alternative hypotheses, then obtain sample data, then make a decision

If a child's height has a z-score of -1.2, this means

his height is 1.2 std dev's below the mean height for his age

The width of a confidence interval for a population mean μ will be:

narrower for 95% confidence than for 98% confidence

Suppose you are told that P(A) = .8, P(A | B) = .5 and P(A ∩ B) = .32. It follows that A and B are:

neither mutually exclusive nor independent

A sampling distribution for p̂ would be obtained by finding ...

the proportions of lots of samples of the same size from the same population

Which of the following is NOT true for a continuous distribution?

the total probability varies with the distribution

Suppose it has been determined that 70% of the planes arrive on time at a certain airport. So X = # of planes that are on time Y = # of planes that are not on time Find the probability that more than 78% of the next 80 planes will be on time. Which of the following is a true statement?

the z-score is positive and the probability is less than .5

A certain university believes that the average number of students taking Introductory Statistics will increase from the current level of 300 students per semester. So: X = # of students taking Stats H0: μ = 300 Ha: µ > 300 Suppose the data lead the university to conclude that the average number of students is increasing, and so they decide to open extra sections and hire more instructors. Which of the following conclusions did they draw?

they rejected H0

Which of the following is NOT an example of statistical inference?

using a pie chart to show people's ice cream flavor preferences

In which of the following problems, would using degrees of freedom be necessary?

x̅ distribution, s = 32.4, n = 30

Which of the following symbols does NOT represent a statistic?

µ