BSTAT CH. 6-10, 14

The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

2.92 ± 02.093(0.16/ √20)

A telephone company wants to estimate, with 95% confidence, the mean number of minutes people in a city spend talking long distance. From past records, the standard deviation is 12 minutes. What is the minimum sample size required if the desired bound on error does not exceed 5 minutes? Assume the length of a call is normally distributed.

23

A sample regression equation is given by = 155 - 34x1 - 12x2. If x1 = 3 and x2 = 2, the predicted value of y would be ________.

29

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 = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736. 0.94

29.70

The t statistic is used to estimate the difference between two population proportions.

False

We use the difference between the sample proportions p1 - p-2 as the point estimator of the difference between two population proportions p1-p2. True or False

False

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. Which of the following hypotheses is relevant to this claim?

H0: p1 - p2 ≤ 0, HA: p1 - p2 > 0

Which of the following pairs of hypotheses are used to test if the mean of the first population is greater than the mean of the second population, using independent random sampling?

H0: µ1 - µ2 ≤ 0, HA: µ1 - µ2 > 0

Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling?

H0: µ1 - µ2 ≥ 0, HA: µ1 - µ2 < 0

If the p-value for a hypothesis test is 0.127 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________.

Not reject the null hypothesis

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X = 15) related to P(X < 16)?

P(X < 16) is greater than P(X = 15)

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?

Reject Ho; we can conclude that the mean differs from zero.

In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size.

True

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

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75.

n = 139

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is E = 1.4? The population standard deviation is known to be 10.75.

n = 160

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)?

p(X> 16) is greater than p(x < 16)

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________.

reject the null hypothesis

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

0.5

A major department store chain is interested in estimating the average 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: X-bar = $50.50 and S2 = 400. Construct a 90% confidence interval for the average 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 ± $9.09

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 95% confidence interval for the population mean?

(11.5592, 13.4408)

Suppose a sample regression equation is given by = 11 − 0.80x. What is the predicted value of y and residual when x is 2 and y is observed to be 9?

/y = 9.4, -0.4

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 exactly 3.7 hours to construct a soapbox derby car.

0.0000

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power?

0.0478

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 less than 0.55 is ______.

0.1537

A multiple regression model with four explanatory variables is estimated using 25 observations resulting in SSE = 660 and SST = 1,000. Which of the following is the correct value of R2?

0.34

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

Consider the sample regression equation = 12 + 3x1 - 5x2 + 7x3 - 2x4. When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y?

Decrease by 7

The coefficients of each explanatory variable in a multiple linear regression model have the same interpretation as the coefficient of the explanatory variable in a simple linear regression model.

False

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.

Another name for an explanatory variable is the dependent variable

False

For a given confidence level 100(1-a)% and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.

False

In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A stratified sample includes randomly selected clusters from each stratum, which are proportional to the stratum's size.

False

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. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are ______________.

Ho: µ ≤ 3.50, Ha: µ > 3.50

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.To determine whether there has been a decrease in the average number of customers visiting the dealership daily, the appropriate hypotheses are _________.

Ho: µ ≥ 800, Ha: µ < 800

Using the same data set, four models are estimated using the same response variable, however, the number of explanatory variables differs. Which of the following models provides the best fit? Model 1 Model 2 Model 3 Model 4 Multiple R 0.993 0.991 0.936 0.746 R Square 0.987 0.982 0.877 0.557 Adj. R Sq 0.982 0.978 0.849 0.513 Stan. Err. 4043 4463 11615 20878 Obser. 12 12 12 12

Model 1

A recent report claimed that Americans are retiring later in life (U.S. News & World Report, August 17). An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t37 = 1.92. With α = 0.05, she ____________________________________________________.

Rejects the null hypothesis and concludes that the mean retirement age has increased

A ________ is a numerical quantity not computed from the data of a sample and is the size of the critical region used in reaching a decision on whether or not to reject the null hypothesis.

Significance level

Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $22.31 and a 95% confidence interval of[$20.5051, $24.2091]. Which of the following statements is a valid explanation of the confidence interval.

We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 5% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

We cannot conclude that the mean differs or does not differ from zero.

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

We have 99% confidence that we have selected a sample whose interval includes the population mean

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

[ 11.7019, 13.2981]

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 fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that__________________________.

the franchiser does not build on an acceptable site

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if ________.

the price of Product A increases by $1, then we predict the demand to decrease by 20,000