Stats Final
Find the median for the given sample data.In ten trips to Las Vegas, a person had the following net gains:
$ 4731.00
The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Calculate the correlation coefficient, r.
-0.991
Assume that blood pressure readings are normally distributed with a mean of 120 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be greater than 122.
0.0062
Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine boys in ten births.
0.010
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2400 miles. What is the probability a certain tire of this brand will last between 54,960 miles and 55,680 miles?
0.0180
Determine the interquartile range. 3, 7, 8, 5, 12, 14, 21, 13, 18
10
Determine the interquartile range. 3, 12, 17, 2, 21, 14, 14, 8, 45, 31
13
Find the number of standard deviations from the mean. Round your answer to two decimal places. The number of assists per match for the setter on your school's volleyball team has a mean of 55 and a standard deviation of 7 . How many standard deviations from the mean is an outing with 70 assists?
2.14 standard deviations above the mean
The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?
2.28%
Find the sample standard deviation. 22 29 21 24 27 28 25 36
4.8
For the situation above, give a practical interpretation of r2 = .66.
66% of the sample variation in SALARY can be explained by using GMAT in a straight-line model.
Use the regression equation to predict the y -value corresponding to the given x-value. Round your answer to the nearest tenth.The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. What is the best predicted value for y given x=10? Assume that the variables x and y have a significant correlation.
69
According to a Gallup poll, about 90% of all American adults owned a cell phone at the time of the poll. The results are based on telephone interviews with a randomly selected national sample of 998 adults, 18 years and older. What was the population of interest in this Gallup Poll?
All American adults
You want to know how many students at USC Upstate are going to the volleyball game. You survey 50 students. Ten are going to the game. The rest are not going to the game. Identify the population in the study.
All students at USC Upstate.
The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5700 . The distribution of incomes is skewed to the right. Determine the sampling distribution of the mean for samples of size 132 .
Approximately normal, mean = $28,520, standard deviation = $ 496
A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.6 hours. In order to test whether the time to fill out the form has been reduced, a sample of 72 small business owners who annually complete the form was randomly chosen. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.
H0: μ = 6.6Ha: μ < 6.6
A stem- and- leaf diagram is given below for the ages of the patients at a hospital.
Left skewed
The ages of a group of patients being treated at one hospital for osteoporosis are summarized in the frequency histogram below.
Left skewed
Rolling a single die 26 times, keeping track of the numbers that are rolled.
Not binomial: there are more than two outcomes for each trial.
The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude about the percentage of adults in the town whose heights are between 60.1 and 74.1 inches?
The percentage is at least 75 %
A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid?
The population of total compensations of CEOs in the service industry is normally distributed.
The principal of a middle school claims that test scores of the seventh- graders at his school vary less than the test scores of the seventh- graders at a neighboring school, which have variation described by σ = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
The mean age of bus drivers in Chicago is greater than 58.3 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
There is sufficient evidence to support the claim μ > 58.3.
A larger standard deviation means greater variability in the data.
True
An assembly line is operating satisfactorily if fewer than 4% of the phones produced per day are defective. To check the quality of a day's production, the company randomly samples 50 phones from a day's production to test for defects. Define the population of interest to the manufacturer.
all the phones produced during the day in question
A manufacturer claims that the mean amount of juice in its 16oz bottles is 16.1oz. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.
left-tailed
x: 11 -10 -19 5 -17 -4 y:-84 42 94 -52 78 12
negative straight line graph
The names of 7 0 contestants are written on 7 0 cards. The cards are placed in a bag, and three names are picked from the bag.
simple random
Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations.What was the mean commission earned? Round your answer to the nearest cent.
$ 3747.72
The amount of Jen's monthly phone bill is normally distributed with a mean of $ 54 and a standard deviation of $ 8 . Find the first quartile, Q 1 .
$48.64
Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size. Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. An equation describing the relationship was found to be: price = 9161.159 + 77 × size What is the estimated change in the average selling price of a house for an increase in house size of 100 square feet?
$7700
Find the z- scores for which 98% of the distribution's area lies between - z and z.
(- 2.33, 2.33)
Find the z- score for which 99 % of the distribution's area lies between - z and z.
(- 2.575 , 2.575 )
Find the standardized test statistic to test the claim that μ1 ≠ μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that σ1≠σ2. n1 = 11, x1 = 8.4, s1 = 0.76 n2 = 18, x2 = 8.8, s2 = 0.51
-1.546
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.0401.
-1.75
An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2). Let μ1 = average delay for Airline 1 and μ2 = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 9.5 minutes delay with a sample standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a sample standard deviation of 3 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Find the standardized test statistic to test the claim.
-2.33
Find the standardized test statistic to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that σ1=σ2. n1 = 15, x1 = 25.76, s1 = 2.9 n2 = 15, x2 = 28.31, s2 = 2.8
-2.450
What number is missing from the table?
.28
A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.
0.0287
The volume of soda a dispensing machine pours into a 12- ounce can of soda follows a normal distribution with a mean of 12.18 ounces and a standard deviation of 0.12 ounce. The company receives complaints from consumers who actually measure the amount of soda in the cans and claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans contain less than the advertised 12 ounces of soda?
0.0668
Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that he or she makes less than $28,000.
0.0918
A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Number of hours spent in lab Grade (percent) 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 Find the coefficient of determination.
0.112
The brand name of a certain chain of coffee shops has a 46 % recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name.
0.267
A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.
0.3372
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. If 64 women are randomly selected, find the probability that they have a mean pregnancy between 266 days and 268 days.
0.3577
A sporting goods retailer conducted a customer survey to determine its customers primary reason for shopping at their store. What proportion of the customers responded that the merchandise was the reason they shopped at the store?
0.43
Find the z-score that is greater than the mean and for which 70% of the distribution's area lies to its left.
0.53
Find the range for the given data set. The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below 0.457 0.652 0.1250.374 0.305 0.119
0.533 m
Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times.
0.9131
The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 111.8 inches?
0.9192
Human body temperatures are normally distributed with a mean of 98.20 and a standard deviation of 0.62. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.5
0.9826
For the standard normal curve, find the z-score that corresponds to the 90th percentile.
1.28
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.Shaded area is 0.0694.
1.48
the probability distribution below describes the number of thunderstorms that a certain town may experience during the month of August. Let X represent the number of thunderstorms in August. What is the expected value of thunderstorms for the town each August? Round the answer to one decimal place.
1.8
The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.95 ° F. What temperature represents the 95th percentile?
100.16 ° F
How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.4 lb of the population mean, and the population standard deviation is known to be 25 lb.
147
Find the range for the given data set.Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: 5 20 4 14 10
16
Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight 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 x=180.975 and s=143.042. Calculate a 99 % confidence interval for the mean endowment of all private colleges in the United States.
180.975 ± 176.955
A laboratory tested 85 chicken eggs and found that the mean amount of cholesterol was 190 milligrams. Assume that o=11.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.
187.5 to 192.5 milligrams
Find the number of standard deviations from the mean. Round your answer to two decimal places. Mario's weekly poker winnings have a mean of $353 and a standard deviation of $67 . Last week he won $185 . How many standard deviations from the mean is that?
2.51 standard deviations below the mean
Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values correspond to women who lost weight. What is the mean weight change? 3 -8 3 -9 11 -9 14 0 13 -5 14 7
2.8 lb
The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct?
50% of the students sampled had textbook costs that were less than $425
The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?
25% of the students sampled had textbook costs that exceeded $500.
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 27.3 milligrams and standard deviation of 2.1 milligrams for a sample of n=9 cigarettes. Construct a 95 % confidence interval for the mean nicotine content of this brand of cigarette.
27.3 ± 1.614
Scores on an English test are normally distributed with a mean of 37.3 and a standard deviation of 8 . Find the score that separates the top 59% from the bottom 41%
35.5
The random variable X is the number that shows up when a loaded die is rolled. Its probability distribution is given in the table. Round the answer to two decimal places. x: 1 2 3 4 5 6 p(x): 0.16 0.11 0.13 0.13 0.1 0.37
4.01
Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations: 22, 29, 21, 24, 27, 28, 25, 36
4.8
A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 46,800 miles and a standard deviation of 4000 miles. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?
41,680
Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 22.6 16.1 36.1 36.0 23.8 20.3
8.35
Find the sample variance for the given data. Round your answer to one more decimal place than the original data. 11.0 17.6 12.6 11.7 16.5
8.85
Find the mode(s) for the given sample data: 97 25 97 13 25 29 56 97
97
The weekly earnings of students in one age group are normally distributed with a standard deviation of 10 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
97
Two different tests are designed to measure employee productivity (x) and dexterity (y). Several employees were randomly selected and tested, and the results are given below.
= 5.05 + 1.91x
Which of the following statements is not true about the constant standard deviation condition of the linear regression model?
A QQ plot (normal probability plot) can help you determine whether the constant standard deviation condition holds.
A psychologist has designed a test to measure stress levels in adults. She has determined that nationwide the mean score on her test is 28. A hypothesis test is to be conducted to determine whether the mean score for trial lawyers exceeds the national mean score. The hypotheses are H0: μ ≤ 28Ha: μ > 28where μ is the mean score for all trial lawyers. Explain the meaning of a Type I error.
A Type I error would occur if, in fact, μ ≤ 28, but the results of the sampling lead to the conclusion that μ > 28.
A researcher interviews 19 work colleagues who just work in his building.
Convenience
To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day.
Convenience
Both Chebyshev's rule and the empirical rule guarantee that no data item will be more than four standard deviations from the mean.
False
Chebyshev's rule applies to qualitative data sets, while the empirical rule applies to quantitative data sets.
False
The mean of a data set is at the 50th percentile.
False
You want to know how many students at USC Upstate are going to the volleyball game. You survey 50 students. Ten are going to the game. The rest are not going to the game. Identify the sample.
Fifty students who are surveyed.
How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 56 tissues during a cold. Suppose a random sample of 100 people yielded the following data on the number of tissues used during a cold: = 42, s = 18. Identify the null and alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less than 56.
H0: μ ≥ 56 vs. Ha: μ < 56
Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating, x, is a useful linear predictor of raise, y, (in dollar). Consequently, the group considered the straight-line regression model y=a+bx. Using the method of least squares, the faculty group obtained the following prediction equation: y=14,000 + 2,000x Interpret the estimated slope of the line.
For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $2,000.
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 48 °F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.
H 0 : μ = 48 °H 1 : μ ≠ 48 °
Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per gallon in the city. Use μ, the true average mileage of the Libra.
H 0 : μ ≤ 23H 1 : μ > 23
The principal of a middle school claims that test scores of the seventh- graders at her school vary less than the test scores of seventh- graders at a neighboring school, which have variation described by σ = 14.7.
H 0 : σ ≥ 14.7H 1 : σ < 14.7
You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 90% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,630 with a standard deviation of $800. Suppose that the interval is calculated to be ($12,291.23, $12,968.77). How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval?
Increase the sample size but decrease the confidence coefficient.
A pre-election poll was taken during a presidential election, and it turned out that 643 out of 1000 voters said they planned to vote for the Democratic candidate. Based on these numbers, it is predicted that more than 60% of all American voters will vote for the Democratic candidate. Does this statement describe descriptive or inferential statistics?
Inferential statistics
From past figures, it is predicted that 14% of the registered voters will vote in the March primary. Does this statement describe descriptive or inferential statistics?
Inferential statistics
Thirty of the 198 students enrolled in Statistics 101 were asked if they wanted Exam II to be a take-home or an in-class assessment. Twenty, or about 67%, of the students polled indicated a preference for an in-class exam. The professor concluded that the majority of students in Statistics101 would prefer an in-class examination for the second assessment. Did the professor perform a descriptive statistics or an inferential statistics?
Inferential statistics
A randomly selected sample of 1,000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1,000 students surveyed said they had. Which one of the following statements about the number 0.16 is correct?
It is a sample proportion.
A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty- six percent (46%) of the 400 students surveyed answered "yes." Which one of the following statements about the number 46% is correct?
It is a sample statistic.
After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of the meat was spoiled. Determine whether the given value 45,000 kg is a statistic or a parameter.
Parameter
Rolling a single die 53 times, keeping track of the "fives" rolled.
Procedure results in a binomial distribution.
We wish to compare the means of two populations using paired observations. Suppose that d=3.125 sd=2.911 and n=8 and that you wish to test the following hypothesis at the 10% level of significance: H0: μd ≤ 0 against H1: μd > 0.What decision rule would you use?
Reject H0 if test statistic is greater than 1.415.
Suppose you want to test the claim that μ1 = μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that σ1= σ2 . At a level of significance of α = 0.01, when should you reject H0? n1 = 15 n2 = 11 x1 = 23 x2 = 21 s1 = 1.5 s2 = 1.9
Reject H0 if the standardized test statistic is less than -2.797 or greater than 2.797.
For the situation above, write the equation of the least squares line.
SALARY = -92040 + 228 (GMAT)
An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT was created from a set of 25 data points.Which of the following is not an assumption required for the simple linear regression analysis to be valid?
SALARY is independent of GMAT.
In a poll of 50,000 randomly selected college students, 74% answered "yes" when asked "Do you have a television in your dorm room?" Identify the sample and population.
Sample: the 50,000 selected college students; population: all college students
Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish. The sample data were obtained in a study of the relationship between the numbers of years (x) applicants have studied Spanish and their score (y) on the test. The regression analysis is given below.The regression equation is = 31.53333 + 10.90476x.R-sq = 83.0%10 - 2 = 8 degrees of freedomPredictor Coef SE(Coef) t-val P-valConstant 31.53333 6.360418 4.957745 0.00111Number of years 10.90476 1.744054 6.252538 0.00024H0: No linear relationship between the number of years and test score, β = 0.Ha: There is a linear relationship between the number of years and test score, β ≠ 0.Do the data provide sufficient evidence to conclude that the number of years applicants have studied Spanish and their score on the test are independent? Assume α = 0.05.
Since the P-value=0.00024 < 0.05, we reject H0 and conclude that there is an association between the number of years applicants have studied Spanish and their score on the test.
A health and fitness club surveys 40 randomly selected members and found that the average weight of those questioned is 157 lb. Determine whether the given value 157 lb is a statistic or a parameter.
Statistic
Children at a Kindergarten school are divided into three groups: Those who are the oldest/first child (there are 200 of them, call this Group I), those who are the second child (there are 150, call this Group II), and those who are the third (or even fourth or fifth) child (there are 75, call this Group III). The social worker at the school will take a sample to find out how many sleepovers they have had (without parents) at a friend's house. She suspects that first-borns do not get as many as later children, so she decides to take a simple random sample of 15 children from each of the three groups. What sampling technique will be used to obtain the sample of children?
Stratified
A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars). At the 5% significance level, do the data provide sufficient evidence to conclude that at this company the mean salary of female employees is less than the mean salary of male employees? Assume the population variances are equal
Test statistic: t = -0.88. P-value = 0.1942. There is not sufficient evidence to support that at this company the mean salary of female employees is less than the mean salary of male employees.
A coach uses a new technique in training middle distance runners. The times, in seconds, for 8 different athletes to run 800 meters before and after this training are shown below. At the 5% significance level, do the data provide sufficient evidence that the training helps to improve times for the 800 meters?
Test statistic: t = 2.23. P-value = 0.0306. There is sufficient evidence to conclude that the training helps to improve times for the 800 meters.
A survey will be given to 100 students randomly selected from the freshmen class at USC Upstate. What is the sample?
The 100 selected students
A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the sample in this study.
The 1500 community college students contacted
According to a Gallup poll, about 90% of all American adults owned a cell phone at the time of the poll. The results are based on telephone interviews with a randomly selected national sample of 998 adults, 18 years and older. What was the sample in this Gallup Poll?
The 998 adults who participated in the survey.
Fill in the blank. __________ is a method of interpreting the standard deviation of data that have a mound- shaped, symmetric distribution.
The Empirical Rule
A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 99% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What would happen to the confidence interval if the confidence level were changed to 98%?
The interval would get narrower.
Which of the following statements about the sampling distribution of the sample mean is incorrect?
The standard deviation of the sampling distribution is σ.
For the situation above, give a practical interpretation of r = .81.
There appears to be a positive correlation between SALARY and GMAT.
The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. School GMAT Acc. Rate Salary1. Harvard 644 15.0% $63,0002. Stanford 665 10.2 60,0003. Penn 644 19.4 55,0004. Northwestern 640 22.6 54,0005. MIT 650 21.3 57,000..24. Maryland 593 28.1 42,92525. Rochester 605 35.9 44,499The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMATusing the 25 data points in the table are shown below.-----------------------------------------------------------------------a = -92040 b = 228 s = 3213 r2 = .66 r = .81 df = 23 t = 6.67-----------------------------------------------------------------------For the situation above, give a practical interpretation of t = 6.67.
There is evidence (at α = .05) of at least a positive linear relationship between SALARY and GMAT
The mean age of bus drivers in Chicago is 50.6 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
There is not sufficient evidence to reject the claim μ = 50.6.
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 40 °F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and will conduct a hypothesis test to determine whether the true mean temperature differs from this value.
Two-tailed
In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of $22.50. Determine whether a normal distribution or a t- distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expenses is normally shaped.
Use the t- distribution.
A 99% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($135,463, $147,088). Give a practical interpretation of the interval.
We are 99% confident that the mean salary of all CEOs in the electronics industry falls in the interval $135,463 to $147,088.
For the situation above, give a practical interpretation of b = 228.
We estimate SALARY to increase $228 for every 1-point increase in GMAT.
A magazine publisher always mails out a questionnaire six months before a subscription ends. This questionnaire asks its subscribers if they are going to renew their subscriptions. On average, only 10% of the subscribers respond to the questionnaire. Of the 10% who do respond, an average of 44% say that they will renew their subscription. This 10% who respond to the questionnaire are known as what?
a sample statistic.
A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the population of interest in this study.
all community college students in the state of Georgia
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
approximately 16%
The mean SAT verbal score is 462 , with a standard deviation of 98 . Use the Empirical Rule to determine what percent of the scores lie between 462 and 560 . (Assume the data set has a bell- shaped distribution.)
approximately 34%
The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 10. Use the Empirical Rule to find the percentage of scores that lie between 60 and 80. (Assume the data set has a bell- shaped distribution.)
approximately 47.5%
The amount of Jen's monthly phone bill has a roughly bell- shaped distribution with a mean of $ 57 and a standard deviation of $ 9 . What percentage of her phone bills are between $ 30 and $ 84 ?
approximately 99.7%
The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 3.6 cars and a standard deviation of 5 . The number of cars running the red light was observed on 100 randomly chosen days and the mean number of cars calculated. Describe the sampling distribution of the sample mean.
approximately normal with mean = 3.6 and standard deviation = 0.5
The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?
at least 75%
A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3- bedroom house using gas or electric energy had a mean of $112 and a standard deviation of $15 . If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $82 ?
at most 25%
Which of the following statements concerning the linear correlation coefficient are true? A: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. B: If the slope of the regression line is negative, then the linear correlation coefficient is negative. C: The value of the linear correlation coefficient always lies between - 1 and 1. D: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of - 0.82.
b&c
A researcher randomly selected 50 of the nation's middle schools and interviewed all of the teachers at each school.
cluster
As part of a marketing experiment, a department store regularly mailed discount coupons to 25 of its credit card holders. Their total credit card purchases over the next three months were compared to their prior credit card purchases during the previous three months. Determine whether the samples are dependent or independent.
dependent
Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game
discrete
Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day
discrete
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 population
As part of a Masterʹs thesis project, a mathematics teacher is interested in the effects of two different teaching methods on mathematics achievement. She randomly chooses one class of students to learn an algebraic concept using traditional methods and another class of students to learn the same algebraic concept using manipulatives. The teacher then compares their test scores. Determine whether the samples are dependent or independent.
independent
Given H 0 : p ≥ 80% and H a : p < 80%, determine whether the hypothesis test is left- tailed, right- tailed, or two- tailed.
left-tailed
The probability that an individual is left- handed is 0.19 . In a class of 90 students, what is the mean and standard deviation of the number of left- handed students? Round to the nearest hundredth when necessary.
mean: 17.1 ; standard deviation: 3.72
Construct and interpret a boxplot or a modified boxplot as specified. The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Construct a boxplot for the data.
min: 0.4 max: 7.0 q1: 2.1 median: 3.45 q3: 3.8
The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $4450 and the standard deviation is $400 . The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. Which of the following describes the sampling distribution of the sample mean?
normally distributed with a mean of $3500 and a standard deviation of $40
The table below gives the career free- throw percentage and the player height for a sample of NBA basketball players, both past and present. Use technology to compute a p- value and use it to determine whether the regression equation is useful for making predictions about freethrow percentage. Test at the 10% significance level with the hypotheses H 0 : β 1 = 0 and H a : β 1 ≠ 0.
p = 0.04622. Since p < α, reject the null hypothesis. The regression equation is useful for making free throw percentage predictions.
The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N=40,000) workers in order to study their preferences for the various components of a potential package. In this study, methods involving the collection, presentation, and summary of the data are called
parameters
In an area of the South, records were kept on the relationship between the rainfall (in inches) and the yield of cotton (bushels per acre). Identify the explanatory (independent) variable
rainfall in inches
The owner of a professional basketball team claims that the mean attendance at games is over 22,000 and therefore the team needs a new arena. Determine whether the hypothesis test for this claim is left- tailed, right- tailed, or two- tailed.
right-tailed
Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 51 minutes and a standard deviation of 5 minutes. The percentage of time that his commute time exceeds 58 minutes is equal to the area under the standard normal curve that lies to the ___ of ___.
right; 7
Many firms use on- the- job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean of the test scores is 72 . Additional information indicated that the median of the test scores was 79 . What type of distribution most likely describes the shape of the test scores?
skewed to the left
A recent survey by the alumni of a major university indicated that the average salary of 10,500 of its 175,000 graduates was $95,000. Determine whether the given value $95,000 is a statistic or a parameter.
statistic
A researcher wants to know whether athletic men are more flexible than non-athletic men. For this experiment, a man who exercised vigorously at least four times per week was considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics: Athletic men: n = 20, x = 4.3 inches, s = 2.1 inches Non Athletic men: n = 20, x = 3.2 inches, s = 1.0 inches. Assume that all conditions for testing have been met and the population variances are different. Report the test statistic and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.
t = 2.115; p = 0.0219; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men.
Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below, should you use the z-interval procedure, t-interval the procedure, or neither?- The population standard deviation is unknown.- The population is normally distributed.- The sample size is small.
t-interval procedure
As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the population of interest for this study.
the current price (or closing price of a NYSE stock)
As part of an economics class project, students were asked to randomly select 500 New Your Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the variable of interest for this study.
the current price (or closing price of a NYSE stock)
A study is under way in Yosemite National Forest to determine the height of adult American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the variable of interest in the study.
the height of an American pine tree in Yosemite National Forest
For any quantitative data set, the sum (x-the mean of x)=0
true
The mean and the standard deviation of the sampled population are, respectively, 211.7 and 21.9 .n = 64
μ = 211.7 ; σ = 2.7
