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Business Statistics
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A
Trucks pass an automatic scale that monitors 2,000 trucks. This population of trucks has an average weight of 20 tons with a standard deviation of 2 tons. If a sample of 50 trucks is taken, what is
The power of a test is 0.981. What is the probability of a Type II error?
A question is asked of a class of 200 freshmen, and 23% of the students know the correct answer. If a sample of 50 students is taken repeatedly, what is the standard deviation of the mean of the
A game is played repeatedly. A player wins one-fifth of the time. If samples of 40 times the game is played are taken repeatedly, what is the expected value of the mean of the sampling distribution
A virus attacks one in three of the people exposed to it. An entire large city is exposed. If samples of 70 people are taken, what is the expected value of the mean of the sampling distribution of
A virus attacks one in three of the people exposed to it. An entire large city is exposed. If samples of 70 people are taken, what is the standard deviation of the mean of the sampling distribution
A company inspects products coming through its production process, and rejects detected products. One-tenth of the items are rejected. If samples of 50 items are taken, what is the expected value of
A company inspects products coming through its production process, and rejects detected products. One-tenth of the items are rejected. If samples of 50 items are taken, what is the standard deviation
A fishing boat has 1,000 fish on board, with an average weight of 120 pounds and a standard deviation of 6.0 pounds.If sample sizes of 50 fish are checked, what is the probability the fish in a
An experimental garden has 500 sunflowers plants. The plants are being treated so they grow to unusual heights. The average height is 9.3 feet with a standard deviation of 0.5 foot. If sample sizes
A company has 800 employees. The average number of workdays between absence for illness is 123 with a standard deviation of 14 days. Samples of 50 employees are examined. What is the probability a
A maker of yardsticks has an ink problem that causes the markings to smear on 4% of the yardsticks. The daily production run is 2,000 yardsticks. What is the probability if a sample of 100 yardsticks
A college gives a placement test to 5,000 incoming students each year. On the average 1,213 place in one or more developmental courses. If a sample of 50 is taken from the 5,000, what is the
A researcher looks at a large set of data, and concludes the population has a standard deviation of 40. Using sample sizes of 64, the researcher is able to focus the mean of the means of the sample
A company has 1,000 employees. The average number of workdays between absence for illness is 80 with a standard deviation of 11 days. Samples of 80 employees are examined. What is the probability a
A maker of greeting cards has an ink problem that causes the ink to smear on 7% of the cards. The daily production run is 500 cards. What is the probability that if a sample of 35 cards is checked,
Suppose X ~ N(–1, 2). What is the z-score of x = 2?
An experiment with a probability of success given as 0.40 is repeated 100 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will
An experiment with a probability of success given as 0.30 is repeated 90 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have
An experiment with a probability of success given as 0.40 is repeated 100 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will
An experiment with a probability of success given as 0.30 is repeated 90 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have
An experiment with a probability of success given as 0.40 is repeated 100 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will
An experiment with a probability of success given as 0.30 is repeated 90 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have
A multiple choice test has a probability any question will be guesses correctly of 0.25. There are 100 questions, and a student guesses at all of them. Use the normal distribution to approximate the
A multiple choice test has a probability any question will be guesses correctly of 0.25. There are 100 questions, and a student guesses at all of them. Use the normal distribution to approximate the
Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at Lucky claimed to wait in the checkout line until their turn. Let X = time in line. Table 6.1 displays the
Suppose that the value of a stock varies each day from \($16\) to \($25\) with a uniform distribution.a. Find the probability that the value of the stock is more than \($19.b.\) Find the probability
Suppose that you have at your disposal the information below for each of 30 drivers. Propose a model (including a very brief indication of symbols used to represent independent variables) to explain
You want to buy a specific computer. A sales representative of the manufacturer claims that retail stores sell this computer at an average price of \($1,249\) with a very narrow standard deviation of
In order to have a correlation coefficient between traits A and B, it is necessary to have:a. one group of subjects, some of whom possess characteristics of trait A, the remainder possessing those of
Define the Correlation Coefficient and give a unique example of its use.
If the correlation between age of an auto and money spent for repairs is +.90a. 81% of the variation in the money spent for repairs is explained by the age of the autob. 81% of money spent for
Suppose that college grade-point average and verbal portion of an IQ test had a correlation of .40. What percentage of the variance do these two have in common?a. 20b. 16c. 40d. 80
True or false? If false, explain why: The coefficient of determination can have values between -1 and +1.
True or False: Whenever r is calculated on the basis of a sample, the value which we obtain for r is only an estimate of the true correlation coefficient which we would obtain if we calculated it for
Under a "scatter diagram" there is a notation that the coefficient of correlation is .10. What does this mean?a. plus and minus 10% from the means includes about 68% of the casesb. one-tenth of the
The correlation coefficient for X and Y is known to be zero. We then can conclude that:a. X and Y have standard distributionsb. the variances of X and Y are equalc. there exists no relationship
What would you guess the value of the correlation coefficient to be for the pair of variables: "number of man-hours worked" and "number of units of work completed"?a. Approximately 0.9b.
In a given group, the correlation between height measured in feet and weight measured in pounds is +.68. Which of the following would alter the value of r?a. height is expressed centimeters.b. weight
Define a t Test of a Regression Coefficient, and give a unique example of its use.
The correlation between scores on a neuroticism test and scores on an anxiety test is high and positive; thereforea. anxiety causes neuroticismb. those who score low on one test tend to score high on
True or False? If False, correct it: Suppose a 95% confidence interval for the slope β of the straight line regression of Y on X is given by -3.5 < β < -0.5. Then a two-sided test of the hypothesis
True or False: It is safer to interpret correlation coefficients as measures of association rather than causation because of the possibility of spurious correlation.
We are interested in finding the linear relation between the number of widgets purchased at one time and the cost per widget. The following data has been obtained: X: Number of widgets purchased - 1,
Discuss briefly the distinction between correlation and causality.
True or False: If r is close to + or -1, we shall say there is a strong correlation, with the tacit understanding that we are referring to a linear relationship and nothing else.
Consider a sample least squares regression analysis between a dependent variable (Y) and an independent variable (X).A sample correlation coefficient of −1 (minus one) tells us thata. there is no
In correlational analysis, when the points scatter widely about the regression line, this means that the correlation isa. negative.b. low.c. heterogeneous.d. between two measures that are unreliable.
In a linear regression, why do we need to be concerned with the range of the independent (X) variable?
Suppose one collected the following information where X is diameter of tree trunk and Y is tree height. Y 48 24 8 18 6 22 10 30 68 Table 13.3 Regression equation: y; = -3.6 + 3.1. Xi What is your
The manufacturers of a chemical used in flea collars claim that under standard test conditions each additional unit of the chemical will bring about a reduction of 5 fleas (i.e. where X j = amount of
True or False? If False, correct it: Suppose you are performing a simple linear regression of Y on X and you test the hypothesis that the slope β is zero against a two-sided alternative. You have n
An economist is interested in the possible influence of "Miracle Wheat" on the average yield of wheat in a district. To do so he fits a linear regression of average yield per year against year after
An interpretation of r = 0.5 is that the following part of the Y-variation is associated with which variation in X:a. mostb. halfc. very littled. one quartere. none of these
Which of the following values of r indicates the most accurate prediction of one variable from another?a. r = 1.18b. r = −.77c. r = .68
A computer program for multiple regression has been used to fit Part of the computer output includes:a. Calculation of confidence interval for b2 consists of _______± (a student's t value)
An investigator has used a multiple regression program on 20 data points to obtain a regression equation with 3 variables. Part of the computer output is:a. 0.80 is an estimate of ___________.b. 0.10
Name one assumption that must be true.There are two assumptions that must be true in order to perform an F test of two variances.
What is the other assumption that must be true?There are two assumptions that must be true in order to perform an F test of two variances.
State the null and alternative hypotheses.Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They
What is s1 in this problem?Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record
What is s2 in this problem?Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record
What is n?Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20
What is the F statistic?Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their
Is the claim accurate?
State the null and alternative hypotheses.Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far.
What is the F Statistic?Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first
What is the critical value?Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first
At the 5% significance level, do we reject the null hypothesis?Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they
State the null and alternative hypotheses.Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has
What is the F Statistic?Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of
At the 5% significance level, what can we say about the cyclists’ variances?Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds
Write one assumption.There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?
Write another assumption.There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?
Write a third assumption.There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?
Write a fourth assumption.There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?
What is the Sum of Squares Factor?There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?Groups of men from three different areas of the
What is the Sum of Squares Error?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups. Group 1
What is the df for the numerator?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups. Group 1
What is the df for the denominator?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups. Group
What is the Mean Square Factor?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups. Group 1
What is the Mean Square Error?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups. Group 1
What is the F statistic?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups. Group 1 Group 2
What is SSbetween?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups.Girls from four
What is the df for the numerator?Groups of men from three different areas of the country are to be tested for mean weight. The entries in Table 12.13 are the weights for the different groups.Girls
What is MSbetween?Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in Table 12.14 are the goals per game for the different teams. Team 1 Team 2 Team
What is SSwithin?Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in Table 12.14 are the goals per game for the different teams. Team 1 Team 2 Team
What is the df for the denominator?Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in Table 12.14 are the goals per game for the different teams.
What is MSwithin?Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in Table 12.14 are the goals per game for the different teams. Team 1 Team 2 Team
What is the F statistic?Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in Table 12.14 are the goals per game for the different teams. Team 1 Team
Judging by the F statistic, do you think it is likely or unlikely that you will reject the null hypothesis?Girls from four different soccer teams are to be tested for mean goals scored per game. The
An F statistic can have what values?
What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?
What is the df(num)?Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 12.15. Team 1 Team 2 Team 3 Team 4 Team 5
What is the df(denom)?Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 12.15. Team 1 Team 2 Team 3 Team 4 Team
What are the Sum of Squares and Mean Squares Factors?Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 12.15.
What are the Sum of Squares and Mean Squares Errors?Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 12.15.
What is the F statistic?Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 12.15. Team 1 Team 2 Team 3 Team 4
What is the p-value?Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 12.15. Team 1 Team 2 Team 3 Team 4 Team 5
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