Business Stat Final

A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?

1.85

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. Find the mean and standard deviation of the waiting time.

115 seconds and 49.07 seconds

An analyst is forecasting net income for Excellence Corporation for the next fiscal year. Her low-end estimate of net income is $250,000, and her high-end estimate is $350,000. Prior research allows her to assume that net income follows a continuous uniform distribution. The probability that net income will be greater than or equal to $337,500 is _______.

12.5%

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has approximately ______________________.

A 50% chance that the actual return will be greater than 8%

How is the consistency of estimators defined?

A consistent estimator approaches the estimated population parameter as the sample size grows larger.

Consider the following hypotheses that relate to the medical field: H0: A person is free of disease, HA: A person has disease In this instance, a Type I error is often referred to as ___________.

A false positive

Packaged candies have three different types of colors, suppose you want to determine if the population proportion of each color is the same. The most appropriate test is the:

Goodness-of-fit test for a multinomial experiment

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score is more than 230?

0.0618

The probability P(Z < -1.28) is closest to ____.

0.1

Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise?

0.0228

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take more than five hours to construct a soapbox derby car.

0.0228

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriot. What is the probability that, of a sample of 100 Indianapolis residents, at least 15% were rooting for the Patriots in Super Bowl XLVI?

0.0475

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students that receive an A is 0.20 or less is ________.

0.1867

Patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will have to wait more than 10 minutes?

0.2865

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is NOT between 0.20 and 0.30 is _________.

0.3734

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized. The BLS reported in February of 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. For the company's sample, the probability that the proportion of people who are in the labor force is greater than 0.65 is ___________.

0.3821

Open the sheet "Mutual Funds" under Chapter 10 excel files. Test the claim that Fund A has a higher mean return than Fund B. Assume that the variances a of both funds are normally distributed and have equal variances. Let Fund A be population 1 and Fund B be Population 2. What is P-Vaule?

0.384

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough?

0.7734

Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability Professor Elderman's class of 36 has a class average below 78?

0.8143

Find the probability P(-1.96<z<1.96)

0.95

A university has six colleges and takes a poll to gauge student support for a tuition increase. The university wants to insure each college is represented fairly. The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. What is the value of the goodness-of-fit test statistic?

15.64

Open the sheet "Mutual Funds" under Chapter 10 excel files. Test the claim that Fund A has a higher mean return than Fund B. Assume that the variances a of both funds are normally distributed and have equal variances. Let Fund A be population 1 and Fund B be Population 2. What Degree of Freedom value used for this test?

16

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is D = 1.5? The population standard deviation is known to be 10.75.

198

A card dealing machine deals spades (1), hearts (2), clubs (3), and diamonds (4) at random as if from an infinite deck. In a randomness check, 1,600 cards were dealt and counted. The results are shown below. For the goodness-of-fit test, the value of the test statistic is: Suit Observed Spades. 410 Hearts 405 Clubs. 370 Diamonds 415

3.125

In the following table, likely voters' preferences of two candidates are cross-classified by gender. For the chi-square test of independence, the value of the test statistic is:

3.25

The stock price of a particular asset has a mean and standard deviation of $58.50 and $8.25, respectively. Use the normal distribution to compute the 95th percentile of this stock price.

72.07

A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-HAMP modifications, where the bank does not receive a bonus from the federal government. In order to qualify for a HAMP modification, borrowers must meet a set of financial suitability criteria. What type of hypothesis test should we use to test whether borrowers from this particular bank who receive HAMP modifications are more likely to re-default than those who receive non-HAMP modifications?

A hypothesis test for P1-P2

Which of the following is true about statistics such as the sample mean or sample proportion?

A statistic is a random variable.

What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested?

A t test under dependent sampling

The minimum sample size n required to estimate a population mean with 95% confidence and the assumed estimate of the population standard deviation 6.5 was found to be 124. Which of the following is the approximate value of the assumed desired margin of error?

D = 1.1441

Open the sheet "Mutual Funds" under Chapter 10 excel files. Test the claim that Fund A has a higher mean return than Fund B. Assume that the variances a of both funds are normally distributed and have equal variances. Let Fund A be population 1 and Fund B be Population 2. What is your conclusion?

Do not reject Ho, there is not enough evidence to support the claim.

A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Using the p-value approach and α = 0.05, the decision and conclusion are:

Do not reject the null hypothesis, cannot conclude not all of the proportions are the same

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) _______.

Estimate

A portfolio manager claims that the mean annual return on one of the mutual funds he manages exceeds 8%. In order to substantiate his claim, he states that over the past 10 years, the mean annual return for the mutual fund has been 9.5% with a sample standard deviation of 1.5%. Assume annual returns are normally distributed.a. Specify the competing hypotheses to test the portfolio manager's claim.b. Calculate the value of the test statistic.c. At the 5% significance level, use the critical value approach to state the decision rule.d. Is the portfolio manager's claim substantiated by the data? Explain.

H0: mu <,= 8% HA: mu > 8% 0.095-0.08/ 0.015/sqrt 10 =3.16 .0058 < .05 reject

Billy wants to test whether the average speed of his favorite pitcher's fastball differs from the league average of 92 miles per hour. He takes a sample of 36 of the pitcher's fastballs and computes a sample mean of 94 miles per hour. Assume that the standard deviation of the population is 4 miles per hour.a. Specify the null and alternative hypotheses to test Billy's claim.b. Calculate the value of the test statistic and the p-value.c. At the 5% significance level, can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average?d. At the 1% significance level, can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average?

H0: mu = 92 HA: mu =/ 92 94-92/ 4/sqrt 36 =3 3 > 1.96 reject null hypothesis conclude that Billy's favorite pitcher's fastball speed differs from the league average

A philanthropic organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the philanthropic organization surveyed for nine months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed.a. Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased since the wells were put in place.b. Calculate the value of the test statistic and the p-value.c. At the 5% significance level, can you conclude that the number of babies falling ill due to typhoid has decreased? Explain.

H0: mu >,= 120 HA: mu < 120 90-120/40 sqrt 9 = - 2.25 reject null hypothesis, conclude that that the number of babies falling ill due to typhoid has decreased

Massachusetts Institute of Technology grants pirate certificates to those students who successfully complete courses in archery, fencing, sailing, and pistol shooting ("MIT Awards Pirate Certificates to Undergraduates," Boston Globe, March 3, 2012). Sheila claims that those students who go on to earn pirate certificates are able to hit a higher proportion of bull's-eyes during the archery final exam than the course average of 0.15. Specify the null and alternative hypotheses to test her claim.

H0: p >, = 0.15 HA : p < 0.15

Open the sheet "Mutual Funds" under Chapter 10 excel files. Test the claim that Fund A has a higher mean return than Fund B. Assume that the variances a of both funds are normally distributed and have equal variances. Let Fund A be population 1 and Fund B be Population 2. Select the correct hypotheses:

H0: µ1 - µ2 ≤ 0, HA: µ1 - µ2 > 0

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) __________.

Is constant for all x between a and b, and 0 otherwise

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been _______ and the probability of making an error would have been ________.

Narrower, unchanged

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is a=0.05 , then the correct conclusion is to ____________________.

Not reject the null hypothesis

What is the purpose of calculating a confidence interval?

Provides a range of values that, with a certain level of confidence, contains the population parameter of interest

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1000 people between the ages of 16 and 24 and found 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the decision is to ____________.

Reject H0; we can conclude that the high school dropout rate has decreased

In the following table, individuals are cross-classified by their age group and income level. Using the p-value approach and α = 0.05, the decision and conclusion are:

Reject the null hypothesis, age and income are dependent

The null hypothesis in a hypothesis test refers to _____________.

The default state of nature

Which of the following does not represent a continuous random variable?

The number of customer arrivals to a bank between 10 am and 11 am.

Two or more random samples are considered independent if ____________.

The process that generates one sample is completely separate from the process that generates the other sample

For the chi-square test of a contingency table, the expected cell frequencies are found as:

The row total multiplied by the column total divided by the sample size

For a multinomial experiment, which of the following is not true?

The trials are dependent

The chi-square test of a contingency table is a test of independence for:

Two qualitative variables

A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of a Type I and Type II error using the null hypothesis "the individual has not taken steroids."

Type I: 4%, Type II: 6%

Construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, she has garnered 51% support.

[0.4534, 0.5666]

We draw a random sample of size 25 from the normal population with the variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?

[11.7019, 13.2981]

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount

[45.3637, 62.6363]

For the goodness-of-fit test, the expected category frequencies found are the:

hypothesized proportions

A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1 and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the correct value of the test statistic?

z = 1.5617

Find the z value such that P(Z<z)=0.9082

z=1.33