Stats Final
The numerical value obtained from a statistical test is called the _______________.
test value
The rounding rule for a confidence interval for a proportion is to round off to three decimal places.
true
The t-distribution has a variance that is greater than one.
true
If the equation for the regression line is y' = -4x + 6, then the slope of this line is
-4
A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, z = A drug company claims that over 90% of all physicians recommend their drug. 800 physicians were asked if they recommend the drug to their patients. 39% said yes. H0: p = 0.9.
-48.08
If the equation for the regression line is y = 7x + 8, then a value of x = -2 will result in a predicted value for y of
-6
In a particular city, the average annual salary for secretaries is $28,000. A sample of 40 secretaries from Company A shows an average annual salary of $23,500 with a population standard deviation of $4,500. Secretaries at Company A claim they are paid less than the city average. What is the test value for this claim?
-6.32
Assume that cans of a X-brand of soda are filled so that the actual amount have a mean of 12.00 oz and a standard deviation of 0.11 oz. Find the probability that a sample of 36 cans will have a mean amount will be between 12.11 and 12.19 oz.
0.0000
the total area under the normal curve is always
100%
The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?
15.7%
The average age of a vehicle registered in the United States is 8 years, or 96 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 98 and 100 months? Assume the standard deviation for the population is 15 months.
15.71%
A study of nickels showed that the the standard deviation of the weight of nickels is 250 milligrams. A coin counter manufacturer wishes to find the 98% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 15 milligrams?
1509
A scientist wants to estimate the average depth of a river. She wants to be 99% confident that the estimate is accurate within 3 feet. From a previous study, the standard deviation of the depths measured was 4.54 feet.
16
If the standard deviation of a population is 20 and we want the standard error (the standard deviation of the sample mean) to be 5, then we need to take
16
The average number of mosquitos in a stagnant pond is 70 per square meter with a standard deviation of 12. If 9 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 73.6 mosquitos per square meter. Assume that the variable is normally distributed.
18.4%
A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications. The data collected is shown below. Non-member 58, 42,46,32,25,75,35,63 Member Price, 32, 22, 20, 16, 19, 58, 34, 48 Find the value of Ex^2
19,712
A scientist wants to estimate the average depth of a river. She wants to be 95% confident that the estimate is accurate within 3 feet. From a previous study, the standard deviation of the depths measured was 4.54 feet.
9
If the equation for the regression line is y' = 7x - 5, then a value of x = 2 will result in a predicted value for y of
9
An average department store sells 150 men's suits per year. The men's suit departments at a particular national chain of stores claim that they sell more than the industry average. In a sample of 40 stores, they sold, on the average, 210 suits per year with a standard deviation of 40. What is the test value for this hypothesis?
9.49
X is a normally distributed random variable with a standard deviation of 4.00. Find the mean of X when 64.8% of the area lies to the left of 11.02. (Note: the diagram is not necessarily to scale.)
9.5
X is a normally distributed random variable with a mean of 11 and a standard deviation of 2.0. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. (Note: the diagram is not necessarily to scale.)
9.92
Identify the confidence interval used in the figure below. (shaded on both ends)
90 %
In a sample of 351 bartenders, 48% heard complaints from patrons about work. If the margin of error was 4.4%, what was the confidence level that was used?
90%
A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65?
94.5%
The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary?
966
In a sample of 855 bartenders, 48.0% report hearing complaints from patrons about their jobs. If the margin of error for the proportion of bartenders hearing job complaints is 4.4 percentage points, what is the degree of confidence used?
99%
The national average of times a person checks their email is 47.9 times per month. A random sample of 20 people yielded a mean of 31.1 email checks per month with a standard deviation of 4.5. At the 0.05 level of significance can it be concluded that this differs from the national average?
For a test value of -16.70, the P-value is < 0.05. Reject the null hypothesis.
Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to apply the z-test. The National Weather Service says that the mean daily high temperature for October in a large midwestern city is 56°F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean is actually lower than 56°F. A sample of mean daily high temperatures for October over the past 36 years yields Assume that the population standard deviation is 5.6° F. Perform the hypothesis test at the significance level.
H0 : μ = 56° F Ha : μ < 56° F Test statistic: z = -2.17. Critical value z = -2.33. Fail to reject H0: μ = 56°F. there is not sufficient evidence to support the claim that the mean is less than 56° F.
Perform a hypothesis test for a population proportion using the critical value approach. In a sample of 83 adults selected randomly from one town, it is found that 8 of them have been exposed to a particular strain of the flu. At the 0.01 significance level, test the claim that the proportion of all adults in the town that have been exposed to this strain of the flu differs from the nationwide percentage of 8%.
H0: p = 0.08 Ha: p ≠ 0.08. Test statistic: z = 0.55. Critical values: z = ±2.575. Fail to reject H0: p = 0.08. There is not sufficient evidence to conclude that the proportion of all adults in the town that have been exposed to this strain of the flu differs from 8%.
A hypothesis test is to be performed. Determine the null and alternative hypotheses. In the past, the mean running time for a certain type of flashlight battery has been 9.3The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.
H0: μ = 9.3 hours Ha: μ ≠ 9.3 hours
A hypothesis test is to be performed. Determine the null and alternative hypotheses. Carter Motor Company claims that its new sedan, the Libra, will average better than 24 miles per gallon in the city. Use μ, the true average mileage of the Libra.
H0: μ ≤ 24 Ha: μ > 24
State whether the null hypothesis should be rejected on the basis of the given P-value. P-value = 0.021, a= 0.05, two-tailed test
Reject
Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected?
negative effect
A random sample of 36 shoppers showed that they spend an average of $23.45 per visit at a local mini-mall. The standard deviation of the population is $2.80. Find a 95% confidence interval of the true mean.
( 22.54 , 24.36 )
A sample of 10 pieces of laminate used in the manufacture of a circuit boards was selected, and the amount of warpage (in inches) under a particular condition was determined for each piece, resulting in a sample mean of 0.0567 and a sample standard deviation of 0.0078. Find a 90% C.I. for the true mean warpage.
(0.052, 0.061)
The winning team's scores in 13 high school basketball games were recorded. If the sample mean is 10.4 points and the sample standard deviation is 0.15 points, find the 98% confidence interval of the true mean.
(10.29, 10.51)
12 squirrels were found to have an average weight of 10.5 ounces with a sample standard deviation is 0.25. Find the 95% confidence interval of the true mean weight.
(10.34, 10.65)
A sample of 10 adult elephants has a mean weight of 14,500 lbs with a sample standard deviation of 1000lbs. Construct a 99% confidence interval of the true mean.
(13472,15528)
A study of 70 bolts of carpet showed that their average length was 160 yards. The standard deviation of the population is 6 yards. Which of the following is the 90% confidence interval for the mean length per bolt of carpet?
(158.8,161.2)
A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 19.8 and the sample standard deviation is 0.20, find the 95% confidence interval of the true mean.
(19.62, 19.99)
Using the z table, find the critical value (or values) for an = 0.09 two-tailed test.
+/- 1.69
At a certain university, the average attendance at basketball games has been 2700 spectators per game. The attendance for the first 15 games has been 2500 spectators per game with a standard deviation of 650. The athletic director claims that the attendance is the same as last year. If = .05, what are the critical values?
+/-2.145
A correlation coefficient computed for n=18 and is r=0.692 . Using the t-test for the correlation coefficient, what are the critical values?
+1.746
Compute the correlation coefficient for the data below X values -5 1 5 10 Y values 4 6 -3 2
-0.459
Compute the correlation coefficient for the data below X values -3 1 5 9 14 Y values 3 6 -3 3 -3
-0.600
If the sample mean is 7, the hypothesized population mean is 10, and the population standard deviation is 4, compute the test value needed for the z test.
-0.75
If the equation for the regression line is y' = 6x + 2, then a value of x = -2 will result in a predicted value for y of
-10
Using the z table, find the critical value (or values) for an = 0.021 left-tailed test.
-2.03
Using the z table in Table E of Appendix C, determine the critical value for the left-tailed test with a= 0.02 .
-2.05
A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using α = 0.01?
-2.33
A hypothesis test is to be performed for a population mean with null hypothesis H0: μ = μ0. The test statistic used will be z = . Find the required critical value(s). Find the critical value(s) for a two-tailed test with and draw a graph that illustrates your answer.
-2.33, 2.33
At a certain university, the average attendance at basketball games has been 3025. Due to the dismal showing of the team this year, the attendance for the first 13 games has averaged only 2615 with a standard deviation of 535. The athletic director claims that the attendance is the same as last year. What is the test value needed to evaluate the claim?
-2.76
Find the critical value(s) for the following t-test: n=11, α= 0.01,left- tailed test
-2.764
The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness. 21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21
/PC/>1
A recent report from the American Medical Association claims that for the first time in 10 years, the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample of 64 psychiatrists this year yielded an average salary of $198,630. Is there evidence that the average salary is actually higher than what the American Medical Association reported? At , what is the p-value for a one-sided test?
0.0024
The graph portrays the decision criterion for a hypothesis test for a population mean. The null hypothesis is The curve is the normal curve for the test statistic under the assumption that the null hypothesis is true. Use the graph to solve the problem. A graphical display of the decision criterion follows. Determine the significance level.
0.005
What is the value of α used in describing the confidence interval shown below. (<------- 98%------>)
0.02
the average number is milligrams of sodium in a certain brand of microwave frozen dinners is 650 mg, and the standard deviation is 32 mg. Assume the variable is normally distributed. If a sample of 10 dinners is selected, find the probability that the mean of the sample will be larger than 670 mg.
0.0239
Compute the value of the correlation coefficient. X: 55,42,47,56,44 Y: 222, 195, 216, 232, 201
0.049
Find the P-value for the test value. t = 1.619, n = 23, right-tailed
0.0598
A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse?
0.139 < p < 0.201
A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65. Reference: Reference for the following two questions. Find the P-value for the test.
0.0668
The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered only cheese pizza. What is the 99% confidence interval of the true proportion of customers who order only cheese pizza?
0.075 < p < 0.300
The average gas mileage of a certain model car is 30 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 2.1, find the probability that a car has a gas mileage of between 29.8 and 30.3 miles per gallon.
0.09
The length of country and western songs is normally distributed and has a mean of 170 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 16 songs will have mean length of 158.30 seconds or less. Assume the distribution of the lengths of the songs is normal.
0.12
A random sample of 75 printers discovered that 15 of them were being used in small businesses . Find the 90% limit for the population proportion of printers that are used in small businesses.
0.124 < p < 0.276
During the month of August, the average temperature of a lake next to a local college is 72 . 5 degrees with a standard deviation of 2 . 3 degrees. For a randomly selected day, find the probability that that the temperature of the lake is more than 75 degrees. (Assume normal distribution)
0.1401
If the length of country and western songs has mean 190 seconds and standard deviation 40 seconds, then the probability that a random selection of 9 songs will have mean length of 177.07 seconds or less is
0.1660
If p is equal to 0.79, then q is equal to ______.
0.21
The GPA's of all students at a large college have an approximately normal distribution with a mean of 3.05 and a standard deviation of 0.25. Find the probability that the mean GPA of a random sample of 16 students selected from the college is 3.10 or higher.
0.2119
The average price of a textbook at a local college is $95.80 with a standard deviation of $9. What is the probability that a student will pay, on a randomly selected book, between $83 and $91 ? (Assume the variable is normally distributed)
0.2203
If the sample mean is 11, the hypothesized population mean is 10, and the population standard deviation is 4, compute the test value needed for the z test.
0.25
Find the probability P(0.36 < z < 1.43) using the standard normal distribution.
0.2831
According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. At , what is the test value?
0.30
Find the probability P(0.26 < z < 1.33) using the standard normal distribution.
0.3057
Assume that men's weights are normally distributed with a mean of 172 lb and standard deviation of 29 lb (National Health Survey) If 50 men are randomly selected, find the probability that they have a mean weight less than 170 lb
0.3156
A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?
0.316 < p < 0.384
A recent study of 750 internet users in Europe found that 35% of internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the internet?
0.316 < p < 0.384
Find the probability P(z < -0.46) using the standard normal distribution.
0.3228
Find the probability P(z < -0.36) using the standard normal distribution.
0.3594
If the correlation coefficient r is equal to 0.611, find the coefficient of determination.
0.373
Find the area under the standard normal distribution curve between z=-3 and z= -.09.
0.4628
Find the area under the standard normal distribution curve between z = 0 and z = 2.16. (RIGHT SIDE SHADED)
0.4846
Using the normal distribution curve shown in the figure below, find the area under the curve between and ?
0.4846
On a daily run of a bus, the average number of passengers is 48. The standard deviation is 3. Assumethe variable is normally distributed. Find the probability that the bus will have more than 48 passengers.
0.50
Find the area under the standard normal distribution curve to the right of z= -.09.
0.5359
The average length of crocodiles in a swamp is 11.5 feet. If the lengths are normally distributed with a standard deviation of 1.7 feet, find the probability that a crocodile is more than 11 feet long.
0.62
It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?
0.620 < p < 0.780
Find the probability P(-1.09 < z < 1.06) using the standard normal distribution.
0.7176
The average age of doctors in a certain hospital is 51.0 years old with a standard deviation of 10.0 years. If 9 doctors are chosen at random for a committee, find the probability that the mean age of those doctors is less than 53.00 years. Assume that the variable is normally distributed.
0.7257
Find the probability P(z > -0.69)
0.7549
If the correlation coefficient r is equal to 0.452, find the coefficient of nondetermination.
0.796
The average diameter of sand dollars on a certain island is 4.00 centimeters with a standard deviation of 0.60 centimeters. If 16 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 3.85 centimeters. Assume that the variable is normally distributed.
0.841
A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications. The data gathered is shown below. Non-member 58, 42,46,32,25,75,35,63 Member Price, 32, 22, 20, 16, 19, 58, 34, 48 What is the value of the correlation coefficient?
0.857
The average height of flowering cherry trees in a nursery is 11.5 feet. If the heights are normally distributed with a standard deviation of 1.7, find the probability that a tree is less than 13.5 feet tall.
0.88
The average height of flowering cherry trees in a certain nursery is 11 feet. If the heights are normally distributed with a standard deviation of 1.6 feet, find the probability that a tree is less than 13 feet tall.
0.89
A research psychologist wants to estimate, with 99% confidence, the true proportion of college applicants who have parents that have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3.5%?
1,359
The average diameter of sand dollars on a certain island is 4.50 centimeters with a standard deviation of 0.70 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.197 centimeters. Assume that the variable is normally distributed.
0.9032
The average teacher's salary in X-city is $37,230. Assume a normally distribution with standard deviation of the population of $5,100. For a sample of 75 teachers, what is the probability that the sample mean is less than $38,000?
0.9066
If the correlation coefficient r is equal to 0.283, find the coefficient of nondetermination.
0.920
The city of Oakdale wishes to see if there is a relationship between the temperature and the amount of electricity used (in kilowatts). Temp., x Kilowatts, y 73 680 78 760 85 910 98 1,510 93 1,170 81 837 76 600 105 1,800 Reference: Ref 10-1 Compute the value of the correlation coefficient.
0.981
Find the area under the standard normal distribution curve to the left of z= 2.55.
0.9946
John Davis, a manager of a supermarket, wants to estimate the proportion of customers who use food stamps at his store. He has no initial estimate of what the sample proportion will be. How large a sample is required to estimate the true proportion to within 3 percentage points with 98% confidence?
1,509
Compute the standard error of the estimate for the data below. Round to the thousandths place. X: 28, 29, 30, 31, 32, 33 Y: 120.9, 124.95, 129.63, 135.21, 136.95
1.044
Using the z table, find the critical value (or values) for an = 0.12 right-tailed test.
1.18
Using the z table, find the critical value (or values) for an a= 0.12 right-tailed test.
1.18
A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, z = Out of 41 observations, 60% were successes. H0: p = 0.49.
1.409
At a= 0.05, what is the critical value for a right tailed test?
1.65
Find T infinity/2 when n = 17 for the 90% confidence interval for the mean.
1.75
If the equation for the regression line is y = 8x - 6, then a value of x = 2 will result in a predicted value for y of
10
If the standard deviation of a normally distributed population is 20.0 and we take a sample of size 4, then the standard error of the mean is
10.0
A recent poll of 700 people who work indoors found that 278 of them smoke. If the researchers want to be 98% confident of their results to within 3.5%, how large a sample is necessary?
1062
A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary?
1062
A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 500 pounds. At a 80% level, how many elephants need to be weighed so the average weight will be accurate to within 200 pounds?
11
A student looked up the number of years served by 35 of the more than 100 Supreme Court justices. The average number of years served by those 35 justices was 13.8. If the standard deviation of the entire population is 7.3 years, find the 95% confidence interval for the average number of years served by all Supreme Court justices.
11.4 < u < 16.2
What is the value of when x = 3, if the equation of the regression line is y' = 23.1 - 3.8x?
11.7
A lawyer researched the average number of years served by 45 different justices on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval for the average number of years served by all Supreme Court justices?
11.7 < u < 15.9
The city of Oakdale wishes to see if there is a relationship between the temperature and the amount of electricity used (in kilowatts). Temp: 73,78,85,98, 93,82, 76, 105 Kilowatts: 680, 760, 910, 1,510, 1,170, 873, 600, 1,800 Reference: Reference for Questions 30-31 Compute the test value for the data in the table.
12.353
The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence. 154 146 158 125 147 151 133 154
13.5 < u < 155.5
If a population has standard deviation 21, what is the minimum sample size to be 99% confident that the error should be accurate to within 1.5?
1305
In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
1330
A report states that 36% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 8% with 95% confidence?
139
A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.7 oz. and the sample standard deviation is 0.70 oz., find the 95% confidence interval of the true mean.
14.2 < u < 15.2
A hypothesis test is to be performed for a population mean with null hypothesis The population is normally distributed and the test statistic used will be z = . Compute the value of the test statistic. A population is normally distributed with a standard deviation . We wish to test the hypotheses H0: μ = 1152.7; h1 = u > 11527. A 105-item sample has a mean x = 1189.8. Compute the value of the test statistic.
14.35
A study of 40 professors showed that the average time they spent creating test questions was 16.5 minutes per question. The standard deviation of the population is 5.8. Which of the following is the 80% confidence interval for the average number of minutes it takes to create a test question?
15.3 < u < 17.7
A sample of 22 adult elephants has a mean weight of 14,500 lbs with a sample standard deviation of 1000lbs. Find the talpha/2 for a 95% confidence interval of the true mean.
2,080
A sample of 22 adult elephants has a mean weight of 14,500 lbs with a sample standard deviation of 1000lbs. Find the talpha/2 for a 95% confidence interval of the true mean.
2.080
What is the critical t-value for a right-tailed test when a= 0.025 and d.f. = 12?
2.179
What is the critical value for a right-tailed t test when α = 0.025 and n = 13?
2.179
Find the value of talpha/2 when d.f.=10 for a 95% confidence interval for the mean.
2.228
What is the critical value for a two-tailed t test when α = 0.02 and n = 19?
2.552
Find the value of talpha/2 when n=18 for a 98% confidence interval for the mean.
2.567
A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, z = A research group wants to determine whether the proportion of car accidents caused by drivers using cell phones has changed from the previous value of 13%. They obtained 10,000 auto accident reports and found that 14% were caused by drivers using cell phones. The hypotheses are where p is the proportion of car accidents caused by drivers using cell phones.
2.974
A sample of six college wrestlers had an average weight of 220 pounds with a sample standard deviation of 12 pounds. Find a 90% confidence interval of the true mean weight of all college wrestlers.
210 < u < 230
A researcher conducted a study of the access speed of 30 hard drives and concluded that his maximum error of estimate was 21. If he were to conduct a second study to reduce the maximum error of estimate to 7, about how many hard drives should he include in his new sample?
270
A report states that 46% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 5% with 90% confidence?
271
A sample of 15 different payroll departments found that the employees worked an average of 310.3 days a year with a sample standard deviation of 23.8 days. What is the 90% confidence interval for the average days worked, , of all payroll departments?
299.5 < u < 321.1
X is a normally distributed random variable with a mean of 5.00. If the probability that X is less than 6.32 is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)
3.00
At a certain university, the average cost of books was $400 per student last semester and the population standard deviation was $75. This semester a sample of 55 students revealed an average cost of books of $435 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?
3.46
A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for the average days worked, , of all payroll departments?
302.4 < u < 318.2
The mean weight of loads of rock is 50.0 tons with a standard deviation of 8.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 49.1 tons. Assume that the variable is normally distributed.
36.32
In order to have the standard error of the mean be 12, one would need to take _______ samples from a normally distributed population with a standard deviation of 24.
4
A study of 45 white mice showed that their average weight was 4.7 ounces. The standard deviation of the population is 0.7 ounces. Which of the following is the 80% confidence interval for the mean weight per white mouse?
4.57 < u < 4.83
The equation of a regression line is y' 4.6 + 3.2x. What is the intercept of this line?
4.6
The average time it takes a person to walk a hiking path is 42 minutes. Because of wind, a group of 20 people walked the path in an average of 46 minutes. The standard deviation, known from previous trips is 5.7 minutes. The groups' claim is the time was different because of wind. Use Find a 90% confidence interval of the true mean. Assume the variable is normally distributed.
43.8 < u < 48.2
Find the probability P(0 < z < 1.67) , using the standard normal distribution
45.25%
A previous analysis of paper boxes showed that the the standard deviation of their lengths is 9 millimeters. A packer wishes to find the 98% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 3 millimeters?
49
A report states that 38% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 5% with 98% confidence?
511
An economics professor randomly selected 100 millionaires in the United States. The average age of these millionaires was 54.8 years with a standard deviation of 7.9 years. What is the 95% confidence interval for the mean age, , of all United States millionaires?
53.3 < u < 56.3
A college believes that 24% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3 percentage points with 90% confidence?
552
If X is a normal random variable with mean 9 and standard deviation 4.0, then find the value x such that P(Z > x) is equal to .7054, as shown below. (Note: the diagram is not necessarily to scale.)
6.84
If the correlation coefficient is 0.790, what is the explained variation?
62.4%
A random sample of magnesium concentrations (in parts per million, or ppm) in ground water from various locations follows. Estimate the mean concentration of magnesium in ppm with 90% confidence. Assume . 40 83 69 64 117 77 55 96 23 106 26 59 122 20 90 103 68 15 63 117 69 8 89 53 6 113 120 72 40 54 77 46 108 74 93
65.1 < u < 74.0
The average age of doctors in a certain hospital is 48.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 6.0 years. If 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years. Assume that the variable is normally distributed.
65.5%
A study of 75 apple trees showed that the average number of apples per tree was 725. The standard deviation of the population is 100. Which of the following is the 99% confidence interval for the mean number of apples per tree for all trees
695 < u < 755
A study of 75 apple trees showed that the average number of apples per tree was 725. The standard deviation of the population is 100. Which of the following is the 99% confidence interval for the mean number of apples per tree for all trees?
695 < u < 755
A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, z = In a school district with 10,000 high school students, 1300 students completed a special class designed to improve their math skills. 780 of these scored better than the district-wide median on a standardized math exam. Does the special class have some value? The hypotheses are where p is the proportion of all those taking the special class who score better than the median.
7.211
X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 11.49. (Note: the diagram is not necessarily to scale.)
7.5
7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.
7.7 < u < 9.7
At a local college, a school organization wants to estimate the mean debt of college graduates. It is known that the population standard deviation of the debts of college graduates is $12,800. How large a sample should be selected so that a 95% confidence interval of the estimate is within $900 of the population mean?
778
X is a normally distributed random variable with a mean of 6.0 and a standard deviation of 2.00. Find the value x such that P(X < x) is equal to 0.86. (Note: the diagram is not necessarily to scale.)
8.16
All tutors that are employed at a local college must take a test and must score in the top 20%. If the scores are normally distributed with a mean of 78 and a standard deviation of 5, what is the cutoff score to be hired?
82.2
A report states that 46% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage points with 98% confidence?
843
Assume that a 90% confidence interval for the mean is (16.0, 19.0). Then a hypothesis test of = 17.0 at 0.10 would result in
Accepting the null hypothesis because 17.0 is between 16.0 and 19.0
It is estimated that the average annual salary for a registered nurse is $46,000 with a standard deviation of $1,800. If 9 random samples of 40 nurses each are randomly selected, the probability that the average salary of one of these samples is less than $45,000 is
B. 0.0002
Ten pairs of points yielded a correlation coefficient of 0.790. If , which of the following statements is correct if ? (Do not calculate a t-value.)
Because 0.790 is greater than 0.632, the null hypothesis is rejected.
Stating the hypothesis should be the first step used in hypothesis testing.
True
When computing a confidence interval for a population mean using raw data, round off to two more decimal places than the number of decimal places in the original data.
False
For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified. A manufacturer claims that the mean amount of juice in its bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The hypotheses are: H0: μ = 16.1 ounces Ha: μ < 16.1 ounces Explain the meaning of a Type I error.
Concluding that μ < 16.1 ounces when in fact u - 16.1 ounces
the value of a/2 used in the figure below is 0.02.
False
It has been claimed that at UCLA at least 40% of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at = .01?
Critical Value: -2.33 Do not reject. The claim that at least 40% of the students at U.C.L.A. live on campus is supported by the evidence.
It is estimated that the average annual salary for a registered nurse is $46,000 with a standard deviation of $1,800. If 16 random samples of 25 nurses each are randomly selected, the probability that the average salary of one of these samples falls between $45,640 and $46,360 is
D. 0.6827
State whether the null hypothesis should be rejected on the basis of the given P-value. P-value = 0.242, a= 0.05, one-tailed test
Do not reject
Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to apply the z-test. The Maine Department of Natural Resources reported that the mean weight of lobsters trapped in the state is 1.7 pounds. Carl Lewis is a lobster trapper off the coast of Maine. Carl suspects that this figure is too high so he records the weights of a random sample of that he trapped. The mean weight of the lobsters in the sample was Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is lower than Assume that the population standard deviation is 0.6 pounds
Fail to reject H0: μ = 1.7 pounds. There is not sufficient evidence to support the claim that the mean is lower than 1.7 pounds.
A correlation coefficient of 0.961 would mean that the values of x increase as the values of y decrease.
False
A right-tailed test is used when h0: u (greater than/ equal to) k
False
A type I error can occur when the null hypothesis is not rejected.
False
A type II error occurs if one does not reject the null hypothesis when it is __________.
False
Sam Ying, a career counselor, claims the average number of years of schooling for an engineer is 15.8 years. A sample of 16 engineers had a mean of 15 years and a standard deviation of 1.5 years. The test value would be -2.68.
False
The rounding rule for the correlation coefficient requires two decimal places.
False
The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.
False
There is one and only one correct method to perform a hypothesis test procedure.
False
Using a regression line of y' 17.3 +3.4x, a value of x = 3.6 would result in a predicted value of .
False
The ______________________ is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter.
Maximum error of estimate
Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected?
Negative effect
Doctors nationally believe that 80% of a certain type of operation are successful. In a particular hospital, 47 of these operations were observed and 37 of them were successful. At = .05, is this hospital's success rate different from the national average?
No, because the test value -0.22 is in the noncritical region.
Doctors nationally believe that 60% of a certain type of operation are successful. In a certain hospital, 51 of these operations were observed and 52% of them were successful. If = .05, is this hospital's success rate different from the national average?
No, because the test value -1.17 is in the noncritical region.
A political strategist believes that 58% of voters in a certain state support his candidate. He then commisions a poll of 700 voters and 51% of them support his candidate. If = .05, is the political strategist's belief warranted?
No, because the test value -3.75 is in the critical region.
Are the following statements h0=7 and h1 (not equal) 7 valid null and alternative hypotheses?
No, there are no parameters contained in these statements.
Is the statement H0: 16 = 8 a valid null hypothesis?
No, theres is no parameter contained in this statement
Preliminary data analyses indicate that it is reasonable to use a to carry out the specified hypothesis test. Perform the . Use a significance level of α = 0.01 to test the claim that The sample data consists of for which and .
Preliminary data analyses indicate that it is reasonable to use a to carry out the specified hypothesis test. Perform the . Use a significance level of α = 0.01 to test the claim that The sample data consists of for which and .
Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to apply the z-test. A national car insurance company stated that in 1987, the average yearly car insurance cost for a family in the U.S. was $1,716. In the same year, a random sample of 32 families in California resulted in a mean cost of . Does this suggest that the average insurance cost for a family in California in 1987 exceeded the national average? Perform the hypothesis test at a significance level of 10%. Assume that the population standard deviation is $35.50.
Reject H0. There is sufficient evidence to support the claim that the mean insurance cost for California drivers in 1987 exceeded the national average.
Test the significance of the correlation coefficient r at = 0.05 for the data below. X values 54 59 68 76 84 Y values 100 107 116 124 129
Reject p=0 because 15.06 > 3.18
Assume that a 95% confidence interval for the mean is (15.5, 18.5). Then a hypothesis test of = 14.0 at 0.05 would result in
Rejecting the null hypothesis because 14.0 is less than 15.5
Assume that in a hypothesis test with null hypothesis = 14.0 at 0.02, that a value of 11.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval result of
The 98% confidence interval for the mean contains the value 14.0
Assume that in a hypothesis test with null hypothesis = 16.0 at 0.01, that a value of 13.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval result of
The 99% confidence interval for the mean contains the value 16.0
Assume that in a hypothesis test with null hypothesis = 12.0 at 0.01, that a value of 13.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result of
The 99% confidence interval for the mean does not contain the value 12.0
For the conjecture "The average age of students in this class is 22", the null hypothesis is:
The average age of students in this class is 22.
If the correlation coefficient r is equal to 0.750, find the coefficient of determination and the coefficient of nondetermination.
The coefficient of determination is 0.563 and the coefficient of nondetermination is 0.437
Assume that in a hypothesis test with null hypothesis = 14.0 at 0.05, that a value of 11.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result of
There is insufficient information to conclude whether the 90% confidence interval for the mean contains or does not contain the value 14.0
A positive relationship exists when both variables increase or decrease at the same time.
True
A regression line was calculated as y'= 9.7 -3.2x. The slope of this line is -3.2.
True
An interval estimate may or may not contain the value of the parameter being estimated.
True
If the null hypothesis is not rejected when it is false, a type II error has occurred.
True
The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.
True
The normal distribution curve can be used as a probability distribution curve for normally distributed variables.
True
The population correlation coefficient is computed by using all possible pairs of data values taken from a population.
True
A study claims that 60% of basketball injuries occur during games. A head trainer claims that this is too high for his team. His team had 16 injuries last season and only 5 occurred during games. Is his claim correct at
With a test value of -2.35, the P-value < 0.05. Reject the null hypothesis.
Educators claim that 75% of all high school students will attend college next fall. At Beechnut High School, with an enrollment of 818 seniors, a study found 645 will attend college in the fall. At = 0.05, test the claim that at least 75% of all high school students will attend college in the fall. Use the P-value method.
With a test value of 2.54, the P-value < 0.05. Reject the null hypothesis.
A political strategist claims that 56% of voters in Madison County support his candidate. In a poll of 100 randomly selected voters, 50 of them support the strategist's candidate. At = .05, is the political strategist's claim warranted?
Yes, because the test value -1.21 is in the noncritical region.
An average computer mouse inspector can inspect 55 mice per hour with a population standard deviation of 8 mice per hour. The 40 computer mice inspectors at a particular factory can only inspect 50 mice per hour. Does the company have reason to believe that these inspectors are slower than average at α = 0.10?
Yes, because the test value -3.95 falls in the critical region.
Nationwide, the average waiting time until a electric utility customer service representative answers a call is 310 seconds. The Gigantic Kilowatt Energy Company randomly sampled 40 calls and found that, on average, they were answered in 281 seconds with a population standard deviation of 35 seconds. Can the company claim that they are faster than the average utility at α = 0.05?
Yes, because the test value -5.24 falls in the critical region.
A scientist claims that only 67% of geese in his area fly south for the winter. He tags 70 random geese in the summer and finds that 20 of them do not fly south in the winter. If = .05, is the scientist's belief warranted?
Yes, because the test value 0.79 is in the noncritical region.
The average greyhound can reach a top speed of 18.6 meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 45 of her dogs ran, on average, 19.0 meters per second with a population standard deviation of 1.4 meters per second. With α = 0.05, is her claim correct?
Yes, because the test value 1.92 falls in the critical region.
An educator claims that the dropout rate for freshmen in a certain college is more than 20%. Last year, from a random sample of 200 freshmen students 49 withdrew. At 0.10 to support the educator's claim?
Yes, because the test value is in the critical region.
Is the statement h0: u=8 a valid null hypothesis?
Yes, this is a statement that compares a parameter to a value.
Give the term for the number of standard deviations that a particular X value is away from the mean.
Z value
The prediction interval around y' for a specific x is
a confidence interval for the true mean value of the y values that correspond to that x.
As a researcher collects more and more data, the 95% prediction intervals in general
become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate.
The range of the correlation coefficient is from 0 to 1.
true
As the sample size n increases, the shape of the distribution of the sample means taken with replacement from a population with mean μ and standard deviation σ, will approach a normal distribution. This distribution will have a mean of μ and a standard deviation o/n . This is a statement of the _______________________.
central limit theorem
Sam Ying, a career counselor, claims the average number of years of schooling for an engineer is 15.8 years. A sample of 16 engineers had a mean of 15.0 years and a standard deviation of 1.5 years. The test value used in evaluating the claim would be -2.68.
false
The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%.
false
The standard deviation of sample means will be larger than the standard deviation of the population
false
The _________________ correction factor is important if a relatively large number of samples are taken without replacement from a small population.
finite population
For a normal distribution curve with a mean of 9 and a standard deviation of 7, which of the following ranges of the variable will define an area under the curve corresponding to a probability of approximately 34%?
from 9 to 16
An educator claims that the dropout rate for freshmen in a certain college is more than 20%. Last year, from a random sample of 200 freshmen students 49 withdrew. The correct statement of the hypotheses and the claim is
h0: p </= 0.20 and h1: p> 20 (claim)
For the conjecture "The average weight of a cuckoo bird is less than 1.9 pounds", the null and alternative hypotheses are:
h1: u > k
Which type of alternative hypothesis is used in the figure below? (shaded on the right)
h1: u > k
The two variables in a scatter plot are called the
independent variable and dependent variable.
The term z infinity/2 (o/ sqrt n) describes the
maximum error of estimate
Identify the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean?
positively skewed
Stating that the area under the standard normal distribution curve between z = 0 and z = 1.00 is 0.3413, is the same as stating that the _____________ of randomly selecting a standard normally distributed variable z with a value between 0 and 1.00 is 0.3413.
probability
If the majority of data values fall to the left of the mean, the distribution is
right-skewed
A software company allows their programmers to work from home an average of 20 hours per week. A department of 15 programmers work a mean of 22 hours per week from home with a standard deviation of 5.6 hours. At is their sufficient evidence to conclude a difference? Give a 95% confidence interval for the true mean number of hours working from home.
t = 1.38; The null hypothesis is not rejected. There is not enough evidence to support the claim that programmers do not work 20 hours per week from home. 18.9 < < 25.1
One normal curve has a mean of 22 and a standard deviation of 4. A second normal curve has a mean of 4 and a standard deviation of 22. The curve that is more dispersed, or spread out, is
the second normal curve
Alyson Silvastein, a scientist, reports that the average number of hours a person can go without sleep and still function normally is 29 with a standard deviation of five hours. A sample of 49 people had an average of 31 hours that they could go without sleep and still function normally. The test value for this hypothesis would be 2.8.
true
Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation for the population of 3.9 minutes. Jennifer's margin of error would be 1.4 minutes.
true
The following formula can be used to find a specific value from a data set: X=z*o + u
true
The null hypothesis states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters.
true
When conducting a two-tailed Z -test with a=0.01 , the test value was 2.07. The decision would be: do not reject the null hypothesis.
true
When conducting a two-tailed z test with α = 0.01, the test value was computed to be 2.07. The decision would be to not reject the null hypothesis.
true
In a(n) _____________ test, the null hypothesis should be rejected when the test value is in either of the two critical regions.
two- tailed
One of the characteristics of the t-distribution is that the curve never touches the ____-axis.
x
Nationwide, the average waiting time until a electric utility customer service representative answers a call is 310 seconds. The Gigantic Kilowatt Energy Company randomly sampled 40 calls and found that, on average, they were answered in 281 seconds with a population standard deviation of 35 seconds. Can the company claim that they are faster than the average utility at α = 0.05?
yes, because the test value -5.24 falls in the critical region.
A hypothesis test is to be performed for a population mean with null hypothesis The population is normally distributed and the test statistic used will be z = . Compute the value of the test statistic. You wish to test the claim that μ < 25.0 at the α = 0.05 significance level. In a sample of n = 53, the sample mean is 26.6. Assume that the population standard deviation, c, is 3. Compute the value of the test statistic.
z= 3.88
A recent study claims that business travelers spend an average of $41 per day on meals. A sample of 16 business travelers found that they had spent an average of $45 per day with a standard deviation of $3.65. If , what are the critical values?
± 2.131
A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65. What are the critical values for a two-tailed t test of this claim with α = 0.05?
± 2.131
Using the z table, determine the critical values for a two-tailed test when α = 0.03.
± 2.17
A hypothesis test is to be performed for a population mean with null hypothesis H0: μ = μ0. The test statistic used will be z = . Find the required critical value(s). α = 0.08 for a two-tailed test.
±1.75