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Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 137662: The breaking point of a cable has a standard deviation of 90 lbs. A rndom sample of 90 newly manufactured cables has a mean breaking strnegth of 1900 lbs. Based on tis sample, find a 95% confidnence interval for the true mean.
What is the lower limit of the 95% conidence interval
What is the upper limit of the 95% confidence internal
THan you
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Question 137632: Please help
James Profit wants to take National Widget Company public. He is interested in the relationship between the size of the initial public offering and the price per share. A sample of 10 companies that recently went public revealed the following information:
size ($millions) price per share
9.0 10.0
13.0 12.4 a. The regression equation is: __________
11.0 10.5
14.0 12.8 b. The coefficient of correlation is: ______
8.0 13.6
9.0 11.5 c. The coefficient of determination is: ____
10.0 14.2
12.0 9.7 d. What would Y equal if X equals13? ______
10.0 12.3
7.0 9.6
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Question 137562: Find the mean and standard deviation of the following discrete random variable.
Number of siblings: X| 1 2 3 4 5
Probability P(X=x): |0.200| 0.425| 0.275|0.075|0.025
1 goes on top 0.200 2 goes on top 0.425 etc.
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Question 137823: The engineer in a widget factory wants to test out a new form of raw materials. So a batch of widgets are made in the old manner as a control group and then a batch are made with the new materials as a comparison. If the widget weight is statistically the same on both sets, the new materials will be used. The weights of the 10 old process widgets and the 10 new process widgets are seen below.
Old New
36.19 36.20
35.80 36.62
36.00 36.03
36.19 36.40
36.18 36.44
36.11 36.02
36.13 36.12
36.48 36.56
35.98 36.05
36.40 36.44
1.Define this situation as either a 2 sample test or a paired test. Why?
2.Calculate a test statistic
3.Calculate a p-value
4.Give an accurate statement as to whether or not the new widget material should be used. Use a significance level of 0.05.
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Question 137808: A student takes a 10 question multiple choice test (each with four options, A-D) without studying or attending class. He plans to guess. A score of 6 out of 10 is needed to pass, 8 out of 10 for high pass.
a. What are his chances of passing by guessing?
b. What are his chances of a high pass just by guessing?
c. Should he manage to pass, how likely would it be a high pass?
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Question 137844: Please help, no text book, online class. Thanks in advance, you rock!!!
1. What is the variable used to predict the value of another called?
A) Independent
B) Dependent
C) Correlation
D) Determination
2. Based on the regression equation, we can
A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.
3. What is the range of values for a coefficient of correlation?
A) 0 to +1.0
B) –3 to +3 inclusive
C) –1.0 to +1.0 inclusive
D) Unlimited range
4. What is the general form of the regression equation?
A) Y' = ab
B) Y' = a + bX
C) Y' = a – bX
D) Y' = abX
5. Which value of r indicates a stronger correlation than 0.40?
A) –0.30
B) –0.50
C) +0.38
D) 0
6. Suppose the least squares regression equation is Y' = 1202 + 1133X.
When X = 3, what does Y' equal?
A) 5,734
B) 8,000
C) 4,601
D) 4,050
7. In the least squares equation, Y' = 10 + 20X , the value of 20 indicates
A) the Y intercept.
B) for each unit increase in X, Y increases by 20.
C) for each unit increase in Y, X increases by 20.
8. In the equation Y' = a + bX, what is Y'?
A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X=0
9. Based on the regression equation, we can
A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.
10. If the regression equation is Y' = 2 – 0.4X, what is the value of Y' when X = –3?
A) 0.8
B) 3.2
C) –10.0
D) 14.0
11. In the regression equation, y’ = a + bx what does the letter "b" represent?
A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Value of Y when X=0
12. A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. What is the dependent variable?
A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the above
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Question 137843: I am having a lot of trouble with a couple of questions. Can someone please explain and help me with them?
1) What is the 90% confidence interval for the variance of exam scores for 28 algebra students, if the standard deviation of their last exam is 12.7?
A) 108.6
B) 10.4
C) 123.7
D) 122.8
2) A sample of 23 European countries found the variance on life expectancy was 7.3 years. What is the 95% confidence interval for the variance of life expectancy in Europe?
A) 27.2
B) 5.6
C) 4.4
D) 28.9
Thank you for your help.
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Question 137820: A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person is selected at random, what is the probability that the person will die before the age of 65?
A) 94.52%
B) 82.89%
C) 94.95%
D) 88.49%
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Question 137872: A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At a=.05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
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Question 137871: Does anyone know what the formula for the z test for proportions is???
I have a few more questions that I really need help with solving.
1) Joan moves into her apartment and wants to purchase a new couch. She wants to determine if there is any difference between the average cost of couches at two different stores. Test the hypothesis that there is no difference at a=0.05.
_ Store 1 Store 2
x $650 $730
O $61 $78
n 24 21
2) Stating that the area under the curve between z=0 and z=1.00 is 0.3413 is the same as stating that the _________________ of selecting any z value between 0 and 1.00 is 0.3413.
3) A regression line was calculated as y = 9.7 -3.2x. The slope of this line is -3.2. True or false??
4) The ________________ are the number of values that are free to vary after sample statistic has been computed.
Thank you for any and all help that you can give me. I am really confused.
x
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Question 137957: 10.52 One group of accounting students took a distance learning class, while another group took the
same course in a traditional classroom. At α = .10, is there a significant difference in the mean
scores listed below? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the
test statistic. (d) Make a decision. (e) Use Excel to find the p-value and interpret it.
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Question 137950: Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the
inactive pill.
(a) State the appropriate hypotheses.
(b) Obtain a test statistic and p-value. Interpret the results at α = .01.
(c) Is normality assured?
(d) Is the difference large enough to be important?
(e) What else would medical researchers need to know before prescribing this drug widely? (Data are from Science News 153 [May 30, 1998], p. 343.)
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Question 138015: The probability that Robin Hood hits a target is 5/6. The probability that Little John hits a target is 1/7. If Robin Hood and Little John each shoot one arrow at the target, what is the probability that they both miss?:
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Question 138078: I saw this question posted but there was no answer so I am posting it again, as I am stumped!
Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the
inactive pill.
(a) State the appropriate hypotheses.
(b) Obtain a test statistic and p-value. Interpret the results at α = .01.
(c) Is normality assured?
(d) Is the difference large enough to be important?
(e) What else would medical researchers need to know before prescribing this drug widely? (Data are from Science News 153 [May 30, 1998], p. 343.)
Click here to see answer by stanbon(26259) |
Question 138077: Please help me!
In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate?
(a) State the hypotheses.
(b) State the decision rule and sketch it.
(c) Find the sample proportions and z test statistic.
(d) Make a decision.
(e) Find the p-value and interpret it.
(f ) If statistically significant, do you think the difference is large enough to
be important? If so, to whom, and why?
(g) Is the normality assumption fulfilled? Explain.
Source: The Wall Street Journal, June 26, 1995, p. B1.
Accident Rate for Dallas Fire Trucks
Statistic Red Fire Trucks Yellow Fire Trucks
Number of accidents x1 = 20 accidents x2 = 4 accidents
Number of fire runs n1 =
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Question 138073: Your help is greatly appreciated!
To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference at α = .05?
(a) State the hypotheses for a right-tailed test.
(b) Obtain a test statistic and p-value assuming equal variances.
Interpret these results.
(c) Is the difference in mean scores large enough to be important? (d) Is it reasonable to assume equal variances?
(e) Carry out a formal test for equal variances at α = .05, showing
all steps clearly.
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Question 137992: A researcher collected sample data for 16 women ages 18 to 24. The sample had a mean serum cholestrol level of 188.8, with a standard deviaiton of 8.2. Assuming that serum cholesterol levels for women ages 18 to 24 are normally distributed find 95% confidence interval for the mean serum cholersrol level of all women in this age group, complete the table below
What is the lower limit of the confidence interval?
what is the upper limit of the confidence interval?
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Question 138072: Please help!
A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
(Data are from a project by statistics students Kim Dyer, Amy Pease, and Lyndsey Smith.)
Click here to see answer by stanbon(26259) |
Question 138071: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Crash1
Crash Damage ($)
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
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Question 138129: Please, Please, Please can someone help me with these questions?? I am just totally confused. This is due tommorrow and I have no idea what i am doing. I would appreciate any and all help with these.
1) A pooled estimate of the variance is a weighted average of the variance using the two sample variances and the ___________ of each variance as the weights.
2) If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in the 200 times at bat?
A) 12.64%
B) 11.72%
C) 50.34%
D) 13.14%
3) When the subjects are paired or matched in some way, samples are considered to be____________?
4) What y z value corresponds to the 17% of the data between the mean and the z value?
A) 1.25
B) 0.44
C) 0.52
D) 2.10
5) A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% condidence interval of the true proportion of cars costing over $700,000?
6) Find the probability for P(0 A) 0.4525 or 45.25%
B) 0.4554 or 45.54%
C) 0.4207 or 42.07%
D) 0.3554 or 35.54%
7) Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a standard deviation of 7? A sample of 50 servings of popcorn yields an average of 78 calories. Check Dr. Cuttleman's claim at a=0.05.
8) The Eagle Ridge Contractors Association claims the average price of a home in thier subdivision is $125,150 with a standard deviation of $ 7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. Is there evidence that the costs of homes for sale in this subdivision are actually lower than claimed? Test a=0.05, what is the test value?
A) -1.31
B) 1.31
C) -1.52
D) 1.52
9) Joan moves into her apartment and wants to purchase a new couch. She wants to determine if there is any difference between the average cost of couches at two different stores. Test the hypothesis that there is no difference at a=0.05
Store 1 Store 2
x(sample mean) $650 $730
o(sample deviation) $61 $ 78
n 24 21
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Question 138036: Hi, I need some help with these few problems. Thanks,
1. Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?
A) 78.2% to 81.8%
B) 69.2% to 86.4%
C) 76.5% to 83.5%
D) 77.7% to 82.3%
E) None of the above
2. A market survey was conducted to estimate the proportion of homemakers who could recognize the brand name of a cleanser based on the shape and color of the container. Of the 1,400 homemakers, 420 were able to identify the brand name. Using the 0.99 degree of confidence, the population proportion lies within what interval?
A) 0.250 and 0.350
B) 0.100 and 0.400
C) 0.950 and 0.997
D) 0.268 and 0.332
E) None of the above
3. The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. What is the 95 percent interval for the population mean?
A) 14.7 and 16.9
B) 13.2 and 17.6
C) 10.0 and 20.0
D) 16.1 and 18.1
E) None of the above
4. Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The mean tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?
A) 50,000
B) 3,500
C) (50,000/100)
D) (3,500/100)
E) None of the above
5. For a given confidence interval, what is the interpretation of a 96% confidence level?
A) 96% chance that the given interval includes the true value of the population parameter
B) Approximately 96 out of 100 such intervals would include the true value of the population parameter
C) 4% chance that the given interval does not include the true value of the population parameter
D) Both "a" and "c" are true
E) None of the above is correct
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Question 138186: First time asker-looking for help with the solution to this problem-just don't feel comfortable with the answer I'm getting. Help would be appreciated.
In Utica, Michigan, 205 of 226 school buses passed the annual safety inspection. In Detroit, Michigan, only 151 of 296 buses passed the inspection. (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value. (c) Is normality assured? (d) If significant, is the difference also large enough to be important?
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Question 138196: One more question:I appreciate the assistance!
Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At α = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population?
Correct Answer Frequency
A 8
B 8
C 9
D 11
E 14
Total 50
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Question 138203: A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank’s claim. Use the information given below. State the null and alternative hypotheses, the significance level, the critical value, the test statistic, the decision and conclusion.
Local Bank Competitor Bank
Sample size n1 = 45 n2 = 50
Average Waiting 2.3 min. 2.6 min.
time in minutes
for each sample
Sample standard s1 = 1.1 min. s 2 = 1.0 min.
Deviation of each
sample
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Question 138237: Hi Stan (U ROCK), I have a couple more I'm having trouble with. THANKS,
T F 1. If 40 samples, each of size n=21, were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.
T F 2. A sample of union members was selected and their opinions regarding the proposed management union contract were recorded with 160 out of the 200 members favored the proposed contract. A 95 percent confidence interval for the population proportion ranged from 0. 74 and 0. 85. If the sample were larger, this interval would be larger (wider).
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Question 138250: Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill.
(a) State the appropriate hypotheses.
(b) Obtain a test statistic and p-value. Interpret the results at α = .01.
(c) Is normality assured?
(d) Is the difference large enough to be important?
(e) What else would medical researchers need to know before prescribing this drug widely?
Click here to see answer by stanbon(26259) |
Question 138253: A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.
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Question 138254: The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using
α = .025? (See story.news.yahoo.com accessed June 25, 2004.)
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Question 138258: Hello again, need assistance please!! THANKS A BUNCH - UR a LIFESAVER!!
1. A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were:
3.087, 3.131, 3.241, 3.241, 3.270, 3.353, 3.400, 3.411, 3.437, 3.477
(a) Construct a 90 percent confidence interval for the true mean weight.
(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?
(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel.)
2. In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.
(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.
(b) Why is the normality assumption not a problem, despite the very small value of p?
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Question 138248: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the
resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with
the results shown below. Research question: Are the mean crash damages the same for these three vehicles?
Crash Damage ($)
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
Click here to see answer by stanbon(26259) |
Question 138247: A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
Click here to see answer by stanbon(26259) |
Question 138246: To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference at α = .05?
(a) State the hypotheses for a right-tailed test.
(b) Obtain a test statistic and p-value assuming equal variances. Interpret these results.
(c) Is the difference in mean scores large enough to be important?
(d) Is it reasonable to assume equal variances?
(e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
Click here to see answer by stanbon(26259) |
Question 138210: Help, I can not figure out how to get the confidence interval for a t distribution. I really need step by step instructions.
For example if my sample mean is 2266.333, my standard deviation is 229.109, a random sample of 12 persons, find a 95% confidence interval for the mean number of miles driven. I can't figure this out, help
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