Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 136316: A Cell phone company offers two plans to its subscribers. At the time new subscribers sign up they are asked to provide some demographic information. The mean yearly income for a sample of 42 subscribers to plan A is $57,000 with a standard Deviation of $6,000. For a sample of 50 subscribers to plan B the mean income is $63,000 with a standard deviation of $4,900. At a significance of 0.05 is there a difference in between the two plans?
Ho
H1
Alpha:
CV:
What Formula?
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Question 136335: Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is 0.90. We select four flights from yesterday for study. (Question 50)
a. What is the likelihood all four of the selected flights arrived within 15 minutes of scheduled time?
b. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time?
c. What is the likelihood that none of the selected flights arrived within 15 minutes of the scheduled time?
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Question 136358: A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 51.2. Based on this information, complete the folloiwng staements about the distribution of the scores on the writing section for the recent year.
1. According to Chebyshev's theorem, at least ____% fo the scores lie within 2.5 standard deviations of the mean, 51.2.
2. Suppose that the distribution is bell shaped. If approximately 99.7% of the scores lie between 23.6 and 78.8, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is _____?
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Question 136384: A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary by mall location? (Data are from a project by MBA students Steve Bennett, Alicia Morais, Steve Olson, and Greg Corda.)
Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total
Car 44 49 36 64 193
Minivan 21 15 18 13 67
Full-sized Van 2 3 3 2 10
SUV 19 27 26 12 84
Truck 14 6 17 9 46
Col Total 100 100 100 100 400
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Question 136383: Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned?
Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
0–9 12 8 3 23
10–59 8 4 10 22
60 or more 1 7 11 19
Col Total 21 19 24 64
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Question 136388: Sixty-four students in an introductory college economics class were asked how many credits they
had earned in college, and how certain they were about their choice of major. Research question:
At α = .01, is the degree of certainty independent of credits earned?
Credits Earned very Uncertain Somewhat Certain Very Certain Row Total
0–9 12 8 3 23
10–59 8 4 10 22
60 or more 1 7 11 19
Col Total 21 19 24 64
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Question 136397: A cab company computed its mean fare from O'Hare Airport to a hotel to be $25.35 Based on this information, complete the following statements about the distribution of the cab fare to the hotel.
a. According to Chebyshev's theorem, at least ______% of the fare lies within 1.5 standard deviations of the mean, 25.35 dollars.
b. Suppose that the distribution is bell shaped. If aproximately 99.7% of the fares lie between 14.67 dollars and 36.03 dollars, then the approximate value of the standard deviation for the distribution, according to the empirical rule is ___________
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Question 136403: A college has 64 students. 36 are sophomores, 39 mathematic majors and 6 are neither. A student is picked at random from the class.
a. What is the probability that the student is both a sophomore and a math major?
b. If the student is a sophomore, what is the probability that he is also a math major? Write yor response as fractions. Thank you.
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Question 136415: Hypothesis test for the difference of population means: t test
An industrial plant wants to determine which of two types of fuel, electric or gas, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of plants using electricity, which had a mean cost per unit of and standard deviation of , and plants using gas, which had a mean of and standard deviation of . Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Can we conclude, at the level of significance, that the mean cost per unit for plants using electricity, , is greater than the mean cost per unit for plants using gas, ?
Perform a one tailed test. Carry your intermediate answers to at least three decimal places.
Null hypothesis—Ho:
Alternate Hypothesis—H1:
The type of test statistic:
The value of the test statistic (round to three decimal places)
The p-value (round to three decimal places:
Can we conclude that the mean cost per unit for plants using electricity is greater than the mean cost per unit for plants using gas? Yes or no.
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Question 136381: 15.28 Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic,Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.)
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Question 136428: A newspaper article reported that people spend a mean of 6.5 hours per day watching TV, with a standard deviation of 1.7 hours. A psychologist would like to conduct interviews with the 15% of the population who spend the most time watching TV. She assumes that the daily time people spend watching TV is normally distributed. At least how many hours of daily TV watching is necessary for a person to be eligible for the interview. Carry your intermediate comutations to a least four decimal places. Round your answer to at least one decimal place.
Thank you.
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Question 136377: Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.
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Question 136373: 26. A study regarding the relationship between age and the amount of pressure sales personnel
feel in relation to their jobs revealed the following sample information. At the .01 significance
level, is there a relationship between job pressure and age?
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 20 18 22
25 up to 40 50 46 44
40 up to 60 58 63 59
60 and older 34 43 43
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Question 136372: 12. For many years TV executives used the guideline that 30 percent of the audience were
watching each of the prime-time networks and 10 percent were watching cable stations on
a weekday night. A random sample of 500 viewers in the Tampa–St. Petersburg, Florida,
area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to
the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station.
At the .05 significance level, can we conclude that the guideline is still reasonable?
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Question 136449: Need help on this problem.....
standard normal probabilities
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.
P (Z > -1.53) =
P (-0.90 < Z < 2.12) =
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Question 136446: The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90% confidence interval, what is the value of t?
d. Develop the 90% confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 63 pounds?
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Question 136371: 30. There are four auto body shops in a community and all claim to promptly serve customers.
To check if there is any difference in service, customers are randomly selected from each
repair shop and their waiting times in days are recorded. The output from a statistical software
package is:
Summary
Groups Count Sum Average Variance
Body Shop A 3 15.4 5.133333 0.323333
Body Shop B 4 32 8 1.433333
Body Shop C 5 25.2 5.04 0.748
Body Shop D 4 25.9 6.475 0.595833
ANOVA
Source of Variation SS df MS F p-value
Between Groups 23.37321 3 7.791069 9.612506 0.001632
Within Groups 9.726167 12 0.810514
Total 33.09938 15
Is there evidence to suggest a difference in the mean waiting times at the four body shops?
Use the .05 significance level.
Please help
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Question 136467: A real estate developer is considering investing in a shopping mall on the outskirts of Dallas, Texas. Various parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of families is selected near each proposed mall. Following are the sample results. At the 0.05 significance level, can the developer conclude there is a difference in the mean income? Use the usual 5 step hypothesis testing procedure.
McKinney Richardson Allen Plano
4 2 1 2
8 3 2 3
4 4 3 1
3
a) State the null and alternate hypothesis
b) What is alpha?
c) What is n?
d) What is K?
e) Formulas:
a) SS total=
b) SSE=
c) SST=
d) dfn=
e) dfd=
f) MST=
g) MSE=
h) F=
Thanks in Advance! :-) Also, the numbers in the cities column are listed individualy and vertically. For some reason they get bunched up on the system.
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Question 136368: 8.64 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?
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Question 136486: When a confidence interval for a population mean is constructed from sample data,
A) we can conclude that the population mean is in the interval
B) we can conclude that the population mean is not in the interval
C) we can conclude, with a stated level of confidence, that the population mean is in the interval
D) we cannot make any inferences.
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Question 136493: 9.62 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.comaccessed June 25, 2004.)
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Question 136492: 9.62 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.comaccessed June 25, 2004.)
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Question 136488: 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 136507: I am having problems trying to figure out can you help thanks.
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
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Question 136507: I am having problems trying to figure out can you help thanks.
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
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Question 136511: Please help, no text book.
Consider this problem:
Instructor Dorff wants to test the hypothesis that students who finish an exam earlier .... get a better score.
She kept track of the order of the submission of a recent test;
>> the first 25 papers showed a mean score of 77.1 with std deviation of 19.6
>> the second 24 papers showed a mean score of 69.3 with std deviation of 24.9
>> state the hypothesis for a right tailed test and test at the 0.05 level of significance .. and determine if the difference in scores is significant
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Question 136541: The lifetime of a certain brand of battery is known to have a standard deviation of 23 hours. Suppose that a random sample of 70 such batteries has a mean lifetime of 35.1 hours. Based on this sample, find a 95% confidence interval for the true mean lifetime of all batteries of this brand.
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Question 136538: Need help with this problem thanks
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 136545: hi i need help to this problem
together, carmen molini and jay mccarroll can prepare a catered dinner in 20 hours. working alone, carmen can do the job 5 hours faster than jay. find the time that each person takes to prepare a catered dinner. round to the nearest tenth.
thank you
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Question 136532: A sample of 20 pages was taken without replacement fromthe 1,591-page phone directory Ameritech Pages Plus Yellow pages
On each page, the mean area devoted to display ads was measured (a display as 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
a construct a 95% confidence interval for the true mean
b Why might normatlity be an issue here? c. What sample size would be needed to obtain an error of _+ 10 square millimeters with 99% confidence
d. If this is no a reasonable requirement, suggest one that is. (Data are from a project by MBA student Daniel R. Dalach)
I am new to this and have not been formally trained! Please help.
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Question 136315: The management of the corporation looking at training issues are not convinced that they should switch to toutside consultants for all of their training programs. They want to look at how the two groups compared on the pretest. The relevant data are given below.
Population 1 Population 2
Outside Consultant In House trainer
Sample
Size 30 40
Mean Score on Pretest 4.8 5.2
Std. Dev. on Pretest Score 0.3 0.4
Test to see if there is a mean difference in the pretest scores. Use Alpha 0.05
Ho
H1
Alpha
CV
What Formula?
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Question 136683: You are performing an expirement to determine how well plants grow under different light sources. Out of the 30 plants in the expirement, 12 receive visible lights, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the expirement receives either visible light or ultraviolet light?
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Question 136637: 11. A survey of industrial salespeople who are either self-employed, work for small, medium-sized, or large firms revealed the following with respect to incomes:
Of those who earn less than $20,000, 9 are self-employed, 12 are employed by small firms, 40 by medium size firms, and 89 by large firms.
Of those who earn $20,000 to $39,999, 11 are self-employed, 10 are employed by small firms, 45 by medium size firms, and 104 by large firms.
Of those who earn $40,000 or more, 10 are self-employed, 13 are employed by small firms, 50 by medium size firms, and 107 by large firms.
Using the .05 level of significance, use a chi-square test to test the hypothesis that there is no relationship between the income level of the industrial salespeople and their employment status. Be sure to state the critical value, the test statistic value, and your interpretation of the test results.
12. Multiple regression uses quantitative values to represent variables that are numeric in nature, but occasionally the use of qualitative variables are used to represent conditions of interest. In those cases, the researcher would use (circle one):
a. dummy variables c. systemic variables
b. non-systemic variables d. insulating variables
Thank you, this class is over!
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Question 136703: The mean length of a small counterbalance bar is 43 millimeters. The production supervisor is concerned that the adjustments of the machine producing the bars have changed. He asks the Engineering Department to investigate. Engineering selects a random sample of 12 bars and measures each. The results are reported below in millimeters:
42 39 42 45 43 40 39 41 40 42 43 42
Is it reasonable to conclude that there has been a change in the mean length of the bars? Use the .02 level of significance. Show all 5 steps – interpret your conclusion!
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Question 136634: Please help
5. The following information was gathered for a One-Way ANOVA test at the .05 level of significance:
Treatment 1 Treatment 2 Treatment 3
9 13 10
7 20 9
11 14 15
9 13 14
12 12 15
The critical value for this test is (circle one) : a. 3.68 b. 3.34 c. 3.18 d. 3.89
6. What is the value of the F statistic in the ANOVA test in question 5 above? _____
7. True or False. A data set resulted in a regression equation of Y = 17.08 - 1.16x From the equation we can determine that the X variable is directly related to the Y variable.
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Question 136557: You are interested in whether men participate more than women in political activities, so you survey 632 men and 675 women and ask them how many political events they attended within the past year. Here are your results:
MEN WOMEN
mean = 1.58 mean = 1.42
s.d. = 0.10 s.d. = 0.23
N=432 N=375
With 95% confidence what do you conclude?
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Question 136636: 10. 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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7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 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