Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 175661: Diana has a box containing 6 blue, 8 red, 5 purple, 9 green, and 2 clear marbles that are all the same size and shape. What is the probability of randomly choosing a clear marble on the first pick; replacing it, and then randomly choosing a purple marble on the second pick?
Click here to see answer by gonzo(654)   |
Question 175705: The records of a casualty insurance company show that, in the past, its clients have had a mean of auto accidents per day with a variance of 1.8 . The actuaries of the company claim that the variance of 0.0016 the number of accidents per day is no longer equal to 0.0016 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis Ho and the alternative hypothesis Hi that we would use for this test.
Click here to see answer by stanbon(26259) |
Question 175812: I'm stumped on 2 word problems dealing with probability. Can someone please help me????
Here they are:
1. Suppose a contest offers $1,000 to the person who can guess the winning four digit number. How many possibilities are there?
2. There are 10 women and 8 men in a club. How many different committees of 6 people can be selected from the group if equal numbers of men and women are to be on the committee?
TIA for your help!
Andrew
Click here to see answer by stanbon(26259) |
Question 175855: A TV special said there is a 10 per cent incidence of sexually transmitted disease (STD) among all U.S. teens. A reporter for the Rockville Bugle, looking for a story, surveyed 260 randomly chosen teenagers, and found that 39 had been to a clinic for STD treatment. Use a right-tail test at α = .05.
The test statistic is
The critical value is
The p-value is
Click here to see answer by stanbon(26259) |
Question 175838: 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 175907: Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop. (b) Check the normality assumption (c) Try the Very Quick Rule. Does it work well here? Why, or why not? (d) Why might this sample not be typical?
Click here to see answer by stanbon(26259) |
Question 175906: A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130
Click here to see answer by stanbon(26259) |
Question 175836: 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 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 175835: 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.
Click here to see answer by stanbon(26259) |
Question 176064: Long-term history has shown that 65% of all elected offices in a rural county have been won by Republican candidates. This year there are 5 offices up for public election in the county Let r be the number of public offices won by Republicans.
a) Find P(r) for r=0,1,2,3,4, and 5
b) Make a histogram for the r probability distribution.
c) What is the expected number of Republicans who will win office in the coming election?
d) What is the standard deviation of r?
Click here to see answer by stanbon(26259) |
Question 176170: Question: A heating and ventilation engineer purchases four 1m radiators and three 1.5m radiators at a cost of £159 for a project. In addition he purchases five 1m radiators and two 1.5m radiators at a cost of £134. Determine the cost of both types of radiator.
Click here to see answer by EMStelley(143) |
Question 176170: Question: A heating and ventilation engineer purchases four 1m radiators and three 1.5m radiators at a cost of £159 for a project. In addition he purchases five 1m radiators and two 1.5m radiators at a cost of £134. Determine the cost of both types of radiator.
Click here to see answer by Mathtut(3670) |
Question 176173: Suppose there are 10 items on a true-false test. The person taking the test does not read the questions; he just answers each question randomly. What is the probability of his guessing ALL answers correctly?
I have to come up with a formula type answer for this, but know that he has a 50/50 chance of answering the questions correctly or at least a 1% chance.
Heeelllp!
TIA
Click here to see answer by Mathtut(3670) |
Question 176071: 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
Click here to see answer by stanbon(26259) |
Question 176197: The mean SAT score in mathematics is 508 . The founders of a nationwide SAT preparation course claim that graduates of the course score higher, on average, than the national mean. Suppose that the founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null hypothesis Ho and the alternative hypothesis H1 that they would use.
Quick Help please
Click here to see answer by MathTherapy(336) |
Question 176335: 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 176503:
Which of the following statements is correct?
For a given level of significance, the critical value of Student's t increases as n increases.
A test statistic of t = 2.131 with d.f. = 15 leads to a clear-cut decision in a two-tailed test where α = .05.
It is harder to reject the null hypothesis when conducting a two-tailed test rather than a one-tailed test.
If we desire α = 0.10 then a p-value of 0.13 would lead us to reject the null hypothesis.
Click here to see answer by stanbon(26259) |
Question 176540: At a certain non-profit organization, % of employees are college graduates and % of employees have more than ten years of experience. If % of the organization's employees are either college graduates or have more than ten years of experience (or both), what is the probability that a randomly selected employee will have more than ten years of experience and be a college graduate?
Click here to see answer by stanbon(26259) |
Question 176539: An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events:
Event : The sum is greater than .
Event : The sum is divisible by or (or both).
Write your answers as exact fractions.
Click here to see answer by stanbon(26259) |
Question 176622: 4. Consider the following contingency table:
Under 20 21-30 31-40
Male 12 12 17
Female 13 16 21
a. If one person is selected at random, what is the probability that person is Female? ______
b. If one person is selected at random, what is the probability that person is either under 20 or over 30? _______
c. If one person is selected at random, what is the probability that person is either male or in the age group 21-30? _____
d. If two people are selected at random, what is the probability they are both female? ______
Click here to see answer by solver91311(5072)  |
Question 176611: In Dallas, some fire trucks were painted yello( instead of red) to heighten their visibility. During a test period, the fleeet of red fire trucks made l53,348 runs and had 20 accidents, while the fleet of yellow fire trucks mad l5,035 runs and had 4 accidents.Did the yellow trucks have a significantly lower accident rate?
Click here to see answer by gonzo(654) |
Question 176625: 3. A business owner decides to use a binomial distribution to solve one of his problems. He knows there is a 60 percent probability that he will sell one of his Red Oak floors to any customer who comes into his shop and views the wood. Out of the next 7 people who come into his shop, what is the probability that 3 people will buy a Red Oak floor? ___________ What is the probability that more than four people will buy the Red oak floor? ___________
Click here to see answer by stanbon(26259) |
Question 176621: 1.A normal distribution with a mean of 55 and a standard deviation of 6 is evaluated to solve a business problem. What is the probability that any value in the population is between 55 and 65? ___________. What is the probability that any value in the population is between 45 and 65? ____________.
2. A business owner decides to use a binomial distribution to solve one of his problems. He knows there is a 60 percent probability that he will sell one of his Red Oak floors to any customer who comes into his shop and views the wood. Out of the next 7 people who come into his shop, what is the probability that 3 people will buy a Red Oak floor? ___________ What is the probability that more than four people will buy the Red oak floor? ___________
Click here to see answer by stanbon(26259) |
Question 176538: From the albums released by a musician, the recording company wishes to release in a boxed set. How many different boxed sets are possible, assuming that the order in which the albums are chosen for a boxed set is irrelevant?
Click here to see answer by stanbon(26259) |
Question 176502: John rejected a null hypothesis in a right-tailed test for a mean at α = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that
A)
John did not commit Type I error.
B)
John did not commit Type II error.
C)
John committed neither Type I nor Type II error.
D)
none of the above can definitely be concluded.
Click here to see answer by stanbon(26259) |
Question 176735: Can someone double check my work please.
Two dice are rolled. Find the odds that the score on the dice is either 6 or 12?
6 = (1,5)(2,4)(3,3)(3,3)(4,2)(5,1) = 6/36 = 1/6
12 = (6,6)(6,6) = 2/36 = 1/18
Did I do this right?
Click here to see answer by solver91311(5072) |
Question 176814: There are 35 fish in a pond. We know that 16 of these fish are males, 4 of these males are salmon and there are 8 salmon in the pond. What is the probability that a randomly chosen fish is a salmon, given that it is a male?
Click here to see answer by stanbon(26259) |
Question 176892: A box contain 15 pencils of same shape and size, but with different colors,
3 of them are of black, 6 white, 2 red and 4 yellow. Two pencils are drawn at random.
Find the probability that they are : 1) black or white 2)One red and other black
Click here to see answer by stanbon(26259) |
Question 177065: A bag contains a red, a blue, a yellow, a white, and a green ball. Three balls are drawn out without replacement.
a.) What is the probability that the red and yellow ball are selected?
B.) What is the probability that the two balls are selected in the order listed (red, yellow)?
Click here to see answer by scott8148(3382)  |
Question 177113: Which of the following statements regarding the coefficient of correlation is true?
A) It ranges from -1.0 to +1.0 inclusive
B) It measures the strength of the relationship between two variables
C) A value of 0.00 indicates two variables are not related
D) All of the above
E) None of the above
Which value of r indicates the strongest correlation?
A) -0.30
B) -0.50
C) +0.48 (would C be correct?)
D) 0.00
E) None of the above
What does a coefficient of correlation of 0.70 mean?
A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of nondetermination is 0.30
E) None of the above
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
E) None of the above
If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?
A) Not correlated
B) Dependent on each other
C) Highly correlated
D) All of the above are correct
E) None of the above is correct
What can we say if the coefficient of determination is 0.94?
A) Strength of relationship is 0.94
B) Direction of relationship is positive
C) 94% of total variation in one variable is explained by variation in the other variable
D) All of the above are correct
E) None of the above is correct
What does the coefficient of determination equal if r = 0.89?
A) 0.94
B) 0.89
C) 0.79
D) 0.06
E) None of the above
What does it mean if r = -1.00?
A) Dependent variable can be perfectly predicted by the independent variable.
B) All of the variation in the dependent variable can be accounted for by the independent variable.
C) High values of one variable are associated with low values of the other variable.
D) Coefficient of determination equals one.
E) All of the above are correct
A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 27 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
A) 4.69 C) 4.75
B) 3.75 D) 18.75
E) None of the above
What is the range of values for the coefficient of determination?
A) -1 to +1 inclusive
B) -3 to +3 inclusive
C) -1 to 0 inclusive
D) 0 to +1 inclusive
E) None of the above
In the regression equation, what does the letter "a" represent?
A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) None of the above
Click here to see answer by stanbon(26259) |
Question 177109: Assume the least squares equation is Y = 10 + 20X. What does the value of 10 in the equation indicate?
A) Y intercept
B) For each unit increased in Y', X increases by 10
C) For each unit increased in X, Y' increases by 10
D) None of the above
Assume the least squares equation is Y' = 10 + 20X. What does the value of 20 indicate?
A) Y intercept
B) For each unit increased in X, Y' increases by 20
C) For each unit increased in Y', X increases by 20
D) None the above
Click here to see answer by stanbon(26259) |
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