SCMT FINAL
If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw, how much would you expect to win on average?
$3
An insurance company will insure a $75,000 Hummer for its full value against theft at a premium of $1500 per year. Suppose that the probability that the Hummer will be stolen is 0.0075. Calculate the expected net profit for the insurance company.
$937.50
Find z when the area to the left of z is .05.
-1.645
In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. For the sake of argument, assume that 51 percent of the actual voters in the state support the incumbent governor (p = 0.51). Calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor.
.0082
A random sample of size 1,000 is taken from a population where p = .20. What is Op?
.01265
The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives?
.017
The weight of a product is normally distributed with a mean of four ounces and a variance of .25 squared ounces. What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces?
.0228
Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.2 ounces. The weights of the sugar packages are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?
.0668
In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process, what is the standard deviation of the sampling distribution of the sample mean?
.10
It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected, what is the probability that the sample mean will be less than 0.84 seconds?
.1151
The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed. What is the probability a subscriber will spend no more than 30 minutes reading the paper?
.1170
A multiple-choice test has 30 questions and each one has five possible answers, of which one is correct. If all answers were guesses, find the probability of getting exactly four correct answers.
.1325
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 30.25 and 30.65 inches long?
.1574
Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it no less than 55 feet?
.1587
Twenty coins are tossed. What is the probability of getting exactly 10 heads?
.1762
According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the probability that exactly three of the individuals have group A blood.
.2765
Determine the probability that a 3 will appear twice, if a fair die is rolled 10 times.
.2907
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last more than 1,200 hours?
.3012
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is less than 3.60 m?
.32
Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.3 ounces. The weights of the sugar packages are normally distributed. What is the probability that 9 randomly selected packages will have an average weight in excess of 16.025 ounces?
.4013
Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). What is the variance for this distribution?
.75
An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that at least three troubles will be repaired on the same day?
.8965
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 29.75 and 30.5 inches long?
.9210
A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that fewer than 4 support increased spending on environmental issues.
.9624
In a simple linear regression model, the intercept term is the mean value of y when x equals _____.
0
The mean of a standard normal distribution is always equal to ____________.
0
The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x)?
0
Consider a normal population with a mean of 10 and a variance of 4. Find P(X > 18).
0.00
The standard deviation of a standard normal distribution is always equal to ____________.
1
X has the probability distribution: X - 2 -1 9 1 2 P(X). .2 .2 .2 .2 .2 Compute the expected value of X.
1.8
Find z when the area between 0 and z is .4750.
1.96
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. 225 flight records are randomly selected and the number of unoccupied seats is noted, with a sample mean of 11.6 seats and a standard deviation of 4.1 seats. How many flights should we select if we wish to estimate μ to within 2 seats and be 95 percent confident?
17
If we are testing the difference between the means of two normally distributed independent populations with samples of n1 = 10, n2 = 10, the degrees of freedom for the t statistic is ______.
18
A simple regression analysis with 20 observations would yield ________ degrees of freedom error and _________ degrees of freedom total.
18, 19
In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 95 percent confidence interval for the true mean length of the bolt?
2.769 to 3.231
In testing the difference between the means of two normally distributed populations, if μ1 = μ2 = 50, n1 = 9, n2 = 13, the degrees of freedom for the t statistic equals ___________.
20
On a standard IQ test, the standard deviation is 15. How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5) and we want 97 percent confidence in the results?
4,239
In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. From the 900 respondents, how many indicated that they would not vote for the current governor or indicated that they were undecided?
405
If the sampled population has a mean of 48 and standard deviation of 16, then the mean and the standard deviation for the sampling distribution of Picture for n = 16 are:
48 and 4
The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Calculate the mean of the sampling distribution of the sample mean.
5.2
In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process, What is the probability the mean length of the bolt is at least 3.16 inches?
5.48%
We want to estimate with 99 percent confidence the percentage of buyers of cars who are under 30 years of age. A margin of error of 5 percentage points is desired. What sample size is needed? In an earlier sample, we found a 99 percent confidence interval of buyers under 30 years of age to be [.18, .27].
523
Suppose the distribution of personal daily water usage in New York City is normally distributed with a mean of 15 gallons and a variance of 25 gallons. Because of a current problem with the distribution of water to its citizens, the mayor wants to give a city tax rebate to the 15 percent of the population who use the least amount of water. What should he use as the water limit for a person to qualify for a city tax rebate?
9.825
The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent). The historical records of the company show that over the past 8 years, the average has been that 13 percent of the accounts have been delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent
92.07%
Assuming the same level of significance α, as the sample size increases, the value of tα/2 ___________ approaches the value of zα/2
Always
In testing for the equality of means from two independent populations, if the hypothesis of equal population means is rejected at α = .01, it will __________ be rejected at α = .05.
Always
When determining the sample size, if the value found is not an integer initially, you should ____________ choose the next highest integer value.
Always
In testing the difference between two independent population means, it is assumed that the level of measurement is at least ______________.
An interval variable
The requirement that the probability of success remains constant from trial to trial is a property of the _______________ distribution.
Binomial
The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.
Binomial
____________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed.
Central limit theorem
The binomial distribution is characterized by situations that are analogous to
Coin tossing
As the sample size increases, the variability of the sampling distribution of the mean ______________.
Decreases
As the significance level α increases, the width of the confidence interval _______________.
Decreases
The variable Employment Status, which can take either the value 1 for Employed and 0 for Unemployed, is an example of a _____________ random variable.
Discrete
The area under the curve of a valid continuous probability distribution must ____________.
Equal 1
The _____________ is the range of the previously observed values of x.
Experimental region
A continuous probability distribution that is useful in describing the time or space between successive occurrences of an event is a(n):
Exponential probability distribution.
A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. At α = .05, we would reject the null hypothesis.
False
Alpha (α) is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.
False
Assume that we are constructing a confidence interval for the difference in the means of two populations based on independent random samples. If both sample sizes n1 and n2 = 10, and the distributions of both populations are highly skewed, then a confidence interval for the difference in the means can be constructed using the t test statistic.
False
Based on a random sample of 25 units of product X, the average weight is 102 lbs., and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed. At α = .01, we can reject the null hypothesis.
False
In forming a confidence interval for μ1 - μ2, only two assumptions are required: independent samples and sample sizes of at least 30.
False
In testing the difference between the means of two independent populations, if neither population is normally distributed, then the sampling distribution of the difference in means will be approximately normal, provided that the sum of the sample sizes obtained from the two populations is at least 30.
False
In testing the difference between the means of two normally distributed populations using large independent random samples, the sample sizes from the two populations must be equal.
False
The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.
False
The experimental region is the range of the previously observed values of the dependent variable.
False
The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.
False
The notation Ŷ refers to the average value of the dependent variable Y.
False
When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance α from .05 to .10 will reduce the probability of a Type I error.
False
When conducting a hypothesis test about a single mean, reducing the level of significance (α) will increase the size of the rejection region.
False
When we test H0: p = .2; versus HA: p ≠ .2, with Picture = .26 and n = 100, at alpha = .05, we reject the null hypothesis.
False
A probability distribution of a discrete random variable is expressed as a table, graph, or ___________.
Formula
Which of the following is an advantage of a confidence interval estimate over a point estimate for a population parameter?
Interval estimates take into account the fact that the statistic being used to estimate the population parameter is a random variable.
A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5. The sampling distribution of Picture ____________________.
Is approximately normal
If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour:
Is greater than the proportion earning less than $13 per hour.
For the following hypothesis test, where H0: μ ≤ 10; vs. HA: μ > 10, we reject H0 at level of significance α and conclude that the true mean is greater than 10, when the true mean is really 8. Based on this information, we can state that we have:
Made a Type I error.
When using simple linear regression, we would like to use confidence intervals for the ___________ and prediction intervals for the ___________ at a given value of x.
Mean y-value, individual y-value
When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.
Narrower than
For a given data set, specific value of X, and confidence level, if all the other factors are constant, the confidence interval for the mean value of Y will ___________ be wider than the corresponding prediction interval for the individual value of Y.
Never
For a given hypothesis test, if we do not reject H0, and H0 is true,
No error has been committed.
In testing the difference between two means from two normally distributed independent populations, the distribution of the difference in sample means will be:
Normally distributed
The ____________ hypothesis is not rejected unless there is sufficient sample evidence to do so.
Null
In a simple linear regression model, the slope term is the change in the mean value of y associated with _____________ in x.
One unit increase
If p = .1 and n = 5, then the corresponding binomial distribution is ____________.
Right skewed
The simple linear regression (least squares method) minimizes:
SSE
A confidence interval for the population mean is an interval constructed around the ____________.
Sample mean
Methods for obtaining a sample are called:
Sampling designs
In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the:
Slope of the regression line
For the same value of X (independent variable), the confidence interval for the average value of Y (dependent variable) is __________________ the prediction interval for the individual value of Y.
Smaller than
If a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.
Sometimes
The least squares regression line minimizes the sum of the:
Squared differences between actual and predicted Y values.
The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. We calculated the value of z for a specific box of this brand of cereal, and the z value was negative. This negative z value indicates that:
The fill weight is less than 910 grams.
Which of the following statements about the binomial distribution is not correct?
The random variable of interest is continuous
A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.
True
Based on a random sample of 25 units of product X, the average weight is 102 lbs. and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed. At α = .05, we do not reject H0.
True
Based on a random sample of 25 units of product X, the average weight is 102 lbs. and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. The alternative hypothesis can be written as HA: μ > 100. (Assume the population is normally distributed.)
True
Based on a random sample of 25 units of product X, the average weight is 102 lbs. and the sample standard deviation is 10 lbs. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed. One way of expressing the null hypothesis is H0: μ = 100.
True
If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.
True
In testing the difference between two means from two independent populations, the sample sizes do not have to be equal.
True
The dependent variable is the variable that is being described, predicted, or controlled.
True
The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.
True
The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).
True
We are testing H0: p ≥ .7; versus HA: p < .7. With Picture = .63 and n = 100, at α = .01, we do not reject the null hypothesis.
True
When comparing two population means based on independent random samples, the pooled estimate of the variance is used when there is an assumption of equal population variances.
True
When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance α from .05 to .10 will reduce the probability of a Type II error.
True
When the null hypothesis is not rejected, there is no possibility of making a Type I error.
True
The rejection of a true null hypothesis is called a ______________ error.
Type 1
For a random variable X, the mean value of the squared deviations of its values from their expected value is called its ____________.
Variance
When the level of confidence and sample proportion p remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400.
Wider than
A sample of 2,000 people yielded p = .52. Calculate a 95 percent confidence interval for p.
[.498, .542]
A sample of 2,000 people yielded p = .52. Calculate a 90 percent confidence interval for p.
[.502, .538]
A computer manufacturing company has sent a mail survey to 2800 of its randomly selected customers that have purchased a new personal computer. The survey asked the customers whether or not they were satisfied with the computer. 800 customers responded to the survey. 640 customers indicated that they were satisfied, while 160 customers indicated they were not satisfied with their new computer. Construct a 96 percent confidence interval estimate of the true proportion of customers satisfied with their new computer.
[.771, .829]
In 1995, 13,000 Internet users were surveyed and asked about their willingness to pay fees for access to websites. Of these, 2,938 were definitely not willing to pay such fees. Construct a 95 percent confidence interval for the proportion definitely unwilling to pay fees.
[0.219, 0.233]
A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of 0.996 ounces with a standard deviation of 0.004 ounces. Construct a 98 percent confidence interval for the mean weight of all such candy. Assume that X, the weight of a candy, is distributed normally.
[0.9940, 0.9980]
At the end of 1990, 1991, and 1992, the average prices of a share of stock in a portfolio were $34.83, $34.65, and $31.26 respectively. To investigate the average share price at the end of 1993, a random sample of 30 stocks was drawn and their closing prices on the last trading day of 1993 were observed with a mean of 33.583 and a standard deviation of 19.149. Estimate the average price of a share of stock in the portfolio at the end of 1993 with a 90 percent confidence interval.
[27.646, 39.523]
A manufacturer of personal computers tests competing brands and finds that the amount of energy they require is normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25 percent and the highest 30 percent are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining computers?
[278.86 289.78]
Researchers have studied the role that the age of workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data are: Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 year olds.
[3.97, 4.11]
The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Find the interval that contains 95.44 percent of the sample means.
[5.16, 5.24]
A sociologist develops a test designed to measure attitudes about disabled people and gives the test to 16 randomly selected subjects. Their mean score is 71.2 with a standard deviation of 10.5. Construct the 99 percent confidence interval for the mean score of all subjects.
[63.46, 78.94]
The mean of the binomial distribution is equal to:
np
The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is:
np ≥ 5 and n(1 − p) ≥ 5
The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.
p
A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. The alternative hypothesis is:
p > .66
The population of all _________________ proportions is described by the sampling distribution of p.
sample
The _____ distribution is used for testing the significance of the slope term.
t
When comparing two independent population means by using samples selected from two independent, normally distributed populations with equal variances, the correct test statistic to use is ______.
t
When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the ___________ distribution.
t
Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances.
t = 1.674
In testing the difference between the means of two normally distributed populations using independent random samples, the correct test statistic to use is:
t statistic
We are testing H0: μ = 32; versus HA: μ > 32. If Picture = 36, s = 1.6, and n = 30, at α = .05, we should reject H0.
true
The ___________ of the simple linear regression model is the value of y when the mean value of x is zero.
y-intercept
The number of standard deviations that a value x is from the mean is a(n) ____________.
z score
The t distribution approaches the _______________ distribution as the sample size ___________.
z, increases
A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry. The alternative hypothesis is:
μconsumer > μbanking
If x is a binomial random variable, then the standard deviation of x is given by:
√npq
