MGMT 208 Exam 2

Which of the following is NOT true about the student's t distribution?

It is used to construct confidence intervals for the population mean when the population standard deviation is known.

The probability that a standard normal random variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

True

The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.

True

The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

True

Theoretically, the mean, median, and mode are all equal for a normal distribution.

True

The standard error of the sampling distribution of a sample proportion is , where p is the sample proportion.

False

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 and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

n = 1,784

The mean of the sampling distribution of a sample proportion is the population proportion, π.

True

The number of customers arriving at a department store in a five-minute period has a Poisson distribution

True

Referring to Table 5-4, the probability of at least one accident is ________.

.9

An economist is interested in studying the incomes of consumers in a particular country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the upper end point in a 99% confidence interval for the average income?

$15,364

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield = $180.975 and S = 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

$180.975 ± $119.586

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: =$50.50 and S = 20. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.

$50.50 ± $11.08

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year's rat orders be, assuming this distribution does not change?

$637

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A confidence interval will be obtained for the proportion of cases of recidivism. Part of this calculation includes the estimated standard error of the sample proportion. For this sample, the estimated standard error is ________.

.028

According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. Referring to the above scenario, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

.05050

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be exactly three power outages in a year is ________.

.0892

According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. Referring to the above scenario, the mean of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

.15

According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. Referring to the above scenario, what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

.1596

According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. Referring to the above scenario, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

.5

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is ________.

.9836

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger?

0.0228

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 90 and 95?

0.0441

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

0.200

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that 2 or fewer prefer Brand C is ________.

0.3174

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is ________.

0.3446

X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________.

0.3483

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.

0.7745

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. Referring to the above scenario, for a randomly chosen Monday, what is the probability there will be less than 340 column inches of classified advertisement?

0.8413

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. Referring to the above scenario, for a randomly chosen Monday, what is the probability there will be between 280 and 360 column inches of classified advertisement?

0.9545

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, what is the needed sample size to obtain a 95% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

1,067

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 85% of the possible Z values are smaller than ________.

1.04

The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is ________.

1.16

Referring to Table 5-4, the mean or expected value of the number of accidents is __________.

2.0

The county clerk wants to estimate the proportion of voters who will need special election facilities. The clerk wants to construct a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion. How large a sample must be taken to assure these conditions are met?

196

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

2.500

If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25 where the standard deviation of the sample S = 0.05, the critical value of t will be ________.

2.7969

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?

2.8 minutes

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. Referring to the above scenario, for a randomly chosen Monday, the probability is 0.1 that there will be less than how many column inches of classified advertisements?

294.4

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The average number that you would expect to prefer Brand C is ________.

3

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. Referring to the above scenario, a single Monday is chosen at random. State in which of the following ranges the number of column inches of classified advertisement is most likely to be.

310-330

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, what is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5%?

384

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The variance of the number of power outages is ________.

6

If n = 10 and μ= 0.70, then the mean of the binomial distribution is ________.

7.00

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.25. Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

73

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is no information about the proportion of students who might choose the option. What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

97

Which of the following yields a cluster sample?

All students in a class are divided into groups according to the rows in which they are seated. One of the groups is randomly selected.

Which of the following yields a systematic sample?

All students in a class are divided into groups of 15. One student is randomly chosen from the first group, the remaining observations are every 15th student thereafter.

Which of the following yields a stratified sample?

All students in a class are grouped according to their gender. A random sample of 8 is selected from the males and a separate random sample of 7 is drawn from the females.

The difference between the sample proportion and the population proportion is called the sampling error.

False

The number of customers arriving at a department store in a five-minute period has a binomial distribution.

False

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, the size of the population is 1,500.

False

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, the standard error is 3%.

False

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, you are 99% confidence that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

False

After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. Referring to the above scenario, the parameter of interest is 54/120 = 0.45.

False

After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. Referring to the above scenario, the parameter of interest to the manager is the proportion of potential customers in this sample that recognize the new product.

False

After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. Referring to the above scenario, this interval requires the use of the t distribution to obtain the confidence coefficient.

False

In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be 6 degrees of freedom.

False

The Poisson distribution can be used to model a continuous random variable.

False

Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" as an inference.

In repeated sampling, 95% of the intervals constructed would contain the population mean.

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

It has a normal distribution with the same mean as the population but with a smaller standard deviation.

Which of the following is NOT a reason for the need for sampling?

It is always more informative by investigating a sample than the entire population

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?

Poisson distribution

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.

The expected or average cost for all weekly rat purchases is $13.00.

Which of the following is true about the sampling distribution of the sample mean?

The mean of the sampling distribution is always μ.

Which of the following yields a simple random sample?

The names of 50 students in a class are written on 50 different pieces of paper and put in a hat. The first 15 pieces of paper are selected blindly one at a time without replacing them back in the hat after shuffling the papers thoroughly.

Which of the following about the binomial distribution is NOT a true statement?

The random variable of interest is continuous.

A normal probability plot may be used to assess the assumption of normality for a particular set of data.

True

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, the sampling error is 3%.

True

Another name for the mean of a probability distribution is its expected value.

True

Any set of normally distributed data can be transformed to its standardized form.

True

For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence.

True

If a simple random sample is chosen with replacement, each individual has the same chance of selection on every selection.

True

If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

True

Sampling error can be completely eliminated by taking larger sample sizes.

True

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.05041.

True

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and S = 20. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ?

a t distribution with 14 degrees of freedom

The standard error of the mean

all of the above (decreases as the sample size increases, is never larger than the standard deviation of the population, measures the variability of the mean from sample to sample)

A probability distribution is an equation that

associates a particular probability of occurrence with each outcome.

What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

binomial distribution

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem? An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample 100 of the company's insurance claims. They believe the number of these 100 that are false will yield the information the company desires.

binomial distribution

A 99% confidence interval estimate can be interpreted to mean that

both of the above

To obtain a sample of 10 books in the store, the manager walked to the first shelf next to the cash register to pick the first 10 books on that shelf. This is an example of a

convenience sample.

The Central Limit Theorem is important in statistics because

for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

At U.S. Data Corporation's web site, they advertised that "Because of our commitment to quality and our vast amount of industry knowledge and experience, we have grown to be one of America's leading providers of mailing lists, marketing data, sales leads and research data. We maintain databases of information on consumers and businesses nationwide that set industry standards for mission critical currency, reliability, and accuracy." Trying to reach 500 potential donors for their annual phone donation campaign, a local fire department purchased a list of donors from the company. This list is an example of a

frame.

In its standardized form, the normal distribution

has a mean of 0 and a standard deviation of 1.

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. Referring to the above scenario, 1,500 is the size of the

sample.

Sampling distributions describe the distribution of

statistics.