BSTAT

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ______.

0.0128

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

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. What are the expected value and the standard error for the proportion of students that receive an A?

0.25 and 0.0559

A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is greater than 0.62 is ______.

0.3415

A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is between 0.55 and 0.62 is ______.

0.5047

A random sample of size 100 is taken from a population described by the proportion p = 0.60. What are the expected value and the standard error for the sampling distribution of the sample proportion?

0.600 and 0.049

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. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park?

0.8092

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

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 an approximate ______.

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

Consider a population proportion p = 0.63. a-1. Calculate the expected value and the standard error of P−P− with n = 30. a-2. Is it appropriate to use the normal distribution approximation for P−P− ? b-1. Calculate the expected value and the standard error of P−P− with n = 36. b-2. Is it appropriate to use the normal distribution approximation for P−P− ?

a-1. expected value 0.63 standard error 0.0881 a-2. yes b-1. expected value 0.63 standard error 0.0805 b-2. yes

Let X be normally distributed with mean μ = 143 and standard deviation σ = 34. a. Find P(X ≤ 100). b. Find P(95 ≤ X ≤ 110). c. Find x such that P(X ≤ x) = 0.370. d. Find x such that P(X > x) = 0.890.

a. .1038 b. .0867 c. 131.712 d. 101.282

Find the following probabilities based on the standard normal variable Z. a.P(Z > 0.94) b.P(Z ≤ −2.08) c.P(0 ≤ Z ≤ 1.32) d.P(−0.93 ≤ Z ≤ 2.68)

a. .1736 b. .0188 c. .4066 d. .8201

For a continuous random variable X, P(28 ≤ X ≤ 68) = 0.20 and P(X > 68) = 0.11. Calculate the following probabilities. a.P(X < 68) b.P(X < 28) c.P(X = 68)

a. 0.89 b. 0.69 c. 0.00

Find the following z values for the standard normal variable Z. a.P(Z ≤ z) = 0.8902 b.P(Z > z) = 0.742 c.P(−z ≤ Z ≤ z) = 0.97 d.P(0 ≤ Z ≤ z) = 0.3509

a. 1.23 b. -0.65 c. 2.17 d. 1.04

Consider a population proportion p = 0.15. a. calculate the standard error for the sampling distribution of the sample proportion when n = 23 and n = 53? b. Is the sampling distribution of the sample proportion approximately normal with n = 23 and n = 53? c. Calculate the probability that the sample proportion is between 0.13 and 0.15 for n = 53.

a. 23= .0745 53= .0490 b. 23= no 53= yes c. Proability= 0.1591

The average rent in a city is $1,410 per month with a standard deviation of $290. Assume rent follows the normal distribution. a. What percentage of rents are between $830 and $1,990? b. What percentage of rents are less than $830? c. What percentage of rents are greater than $2,280?

a. 95.44 b. 2.28 c. .14

A random sample is drawn from a population with mean μ = 65 and standard deviation σ = 5.4. a. Is the sampling distribution of the sample mean with n = 16 and n = 32 normally distributed? b. Calculate the probability that the sample mean falls between 65 and 68 for n = 32.

a. No, only the sample mean with n = 32 will have a normal distribution. Correct b. probability .4992

A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $350,000, the company believes that it will be able to get an average sale price of $274,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $11,000. [You may find it useful to reference the z table.] a. What is the probability that the condominium will sell at a price (i) Below $263,000?, (ii) Above $300,000? b. The company is also trying to sell an artist's condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $274,000, but with a higher standard deviation of $15,000. What is the probability that this condo will sell at a price (i) Below $263,000?, (ii) Above $300,000?

a.) Below $263,000= .1587 Above $300,000= .0091 b.) below $263,000=.2367 above $300,000= .0418

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated?

.0912

The probability that a normal random variable is less than its mean is ______.

.5

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

According to a report in USAToday, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?

1.96(0.0632)

A researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.03 for a 95% confidence interval?

1068

A politician wants to estimate the percentage of people who like his new slogan. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval?

151

What is tα/2,dftα⁢/2⁢, df for a 95% confidence interval of the population mean based on a sample of 15 observations?

2.145

What is tα/2,dftα⁢/2⁢, df for a 99% confidence interval of the population mean based on a sample of 25 observations?

2.797

The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with 99% confidence interval and a margin of error within plus or minus $6. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is ______.

239

An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study has estimated this on-time arrival rate as 78.5%. What is the minimum number of arrivals this employee must include in the sample to ensure that the margin of error for a 95% confidence interval is no more than 0.05?

260

Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736.

29.70

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.9394.

374

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

A statistic is a random variable.

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero.

A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.

F

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

F

A parameter is a random variable, whereas a sample statistic is a constant.

F

Examples of random variables that closely follow a normal distribution include the age and the class year designation of a college student.

F

If the expected value of a sample mean equals the population mean, the sample mean is biased.

F

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis."

F

The letter Z is used to denote a random variable with any normal distribution.

F

The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the tdf distribution is similar to the z distribution.

F

Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim.

H0: p ≥ 0.84 and HA: p < 0.84

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university's belief, the appropriate hypotheses are __________.

Ho:p≥0.20,HA:p<0.20

for a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?

If the population standard deviation is greater, the interval is wider.

Which of the following is not a form of bias?

Information from the sample is typical of information in the population.

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed?

Left-tailed

If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ______.

P(-2 ≤ Z ≤ -1)

A continuous random variable is characterized by uncountable values and can take on any value within an interval.

T

A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

T

Bias refers to the tendency of a sample statistic to systematically over-or underestimate a population parameter.

T

In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails.

T

The probability density function of a continuous random variable is the counterpart to the probability mass function of a discrete random variable.

T

The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?

The mean score on the eighth-grade reading comprehension test

What is the purpose of calculating a confidence interval?

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The confidence interval for this hypothesis test would be __________________.

[$16,788.22, $19,611.78]

The average natural gas bill for a random sample of 21 homes in 19810 zip code during the month of March was $311.90 with a sample standard deviation of $51.60. The 90% confidence interval around this sample mean is _______.

[$292.48, $331.32]

Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36, find a 95% confidence interval on the population mean.

[25.8158, 28.1842]

A random sample is drawn from a normally distributed population with mean μ = 19 and standard deviation σ = 1.8. a. Are the sampling distribution of the sample mean with n = 27 and n = 54 normally distributed? b. Calculate the probabilities that the sample mean is less than 19.9 for both sample sizes.

a. Yes, both the sample means will have a normal distribution. b. 27= .9953 54= .9999

A random sample of size n = 60 is taken from a population with mean μ = −11.4 and standard deviation σ = 3. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. b. What is the probability that the sample mean is less than −11? c. What is the probability that the sample mean falls between −11 and −10?

a. expected value -11.4 standard error 0.3873 b. probability 0.8485 c. probability 0.1514

A random sample of size n = 200 is taken from a population with a population proportion p = 0.71. a. calculate the expected value and the standard error for the sampling distribution of the sample proportion. b. What is the probability that the sample proportion is between 0.70 and 0.80? c. What is the probability that the sample proportion is less than 0.70?

a. expected value 0.71 standard error 0.0321 b. probability 0.6191 c. probability 0.3783

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At the 5% significance level, the decision is to ___________.

do not reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

Find the minimum sample size when we want to construct a 90% 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 preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.

n = 73

Selection bias occurs when ______.

portions of the population are excluded from the consideration for the sample

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. At a 5% significance level, the decision is to _________________________________________________________________________.

reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 78%. If it is known that returns are normally distributed with a mean of 4.3%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation?

standard deviation= 5.570

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

t15 = -3.00

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________.

the mean GPA of the university honors students

The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then _______________________________________________.

the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease

According to the central limit theorem, the distribution of the sample means is normal if ______.

the sample size n ≥ 30

A hypothesis test regarding the population mean is based on ________________________________.

the sampling distribution of the sample mean

If the chosen significance level is α = 0.05, then ____________________________________________.

there is a 5% probability of rejecting a true null hypothesis

Nonresponse bias occurs when ______.

those responding to a survey or poll differ systematically from the nonrespondents