Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1206154: On a normal weekend, 14% of those attending Mass at a local Catholic church donate over $200 per week, 26% donate between $100 and $200 per week, and the remaining donate less than $100 per week. At Christmas time, a survey of 226 people attending Masses finds that 28% donate over $200, 49% donate between $100 and $200, and the remaining donate less than $100. When testing (at the 10% level of significance) whether the proportions are different at Christmas time than during other weekends, what is the test statistic (please round your answer to 3 decimal places,show work)
Click here to see answer by CPhill(1959)   |
Question 1206153: Nationally, 60% of American own American cars, 29% of Americans own Asian cars, and the remaing Americans own non-Asian foreign cars. A survey of 206 people in California finds that 51% own American cars, 31% own Asian cars, and the remaining own non-Asian foreign cars. When testing (at the 10% level of significance) whether the proportions in California are the same as the national proportions, what is the test statistic (please round your answer to 3 decimal places, show work)
Click here to see answer by CPhill(1959) |
Question 1205589: At the same distance with the same measuring device, B was measured 8 times. The average measurement result was 202m, with an average square deviation of s=0.7m.
1)Determine the confidence interval for the mathematical expectation of the measurement of distance B with a probability of 0.92.
2)Test the hypothesis: H0: σ^2 ≥ 0.65, H1: σ^2 < 0.65, with a significance level of 0.1.
Click here to see answer by CPhill(1959) |
Question 1205591: After selecting a sample containing 27 observations, it is calculated that
∑X=10
∑Y=2
∑X^2=160
∑Y^2=420
1)Construct the equation of the linear regression.
2)Determine the confidence interval for the coefficient 𝛼 with a significance level of 0.02.
3)Test the hypothesis with a probability of 0.95:
H0: 𝛼 ≤ 0,
H1: 𝛼 > 0.
Click here to see answer by CPhill(1959) |
Question 1205202: 1. Considering the following distribution for blood pressure level of male patients in a given hospital
(in mm Hg).
Values (BP) Frequency (# of patients)
140- 150 17
150- 160 29
160- 170 42
170- 180 72
180- 190 84
190- 200 107
200- 210 49
210- 220 34
220- 230 31
230- 240 16
240- 250 12
Calculate:
a) All the quartiles.
b) Find the 8th deciles.
c) Find the 20th percentiles
Click here to see answer by CPhill(1959) |
Question 1206786: The World Bank records the prevalence of HIV in countries around the world. According to their data, "Prevalence of HIV refers to the percentage of people ages 15 to 49 who are infected with HIV." In one country, the prevalence of HIV is 16.6%. Let X = the number of people you test until you find a person infected with HIV.
What is the probability that you must test 33 people to find one with HIV? (Round your answer to four decimal places.)
What is the probability that you must ask seventeen people? (Round your answer to four decimal places.)
Click here to see answer by CPhill(1959) |
Question 1206788: A group of Martial Arts students is planning on participating in an upcoming demonstration. Seven are students of Tae Kwon Do; eight are students of Shotokan Karate. Suppose that nine students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate students in that first demonstration.
Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.)
Click here to see answer by CPhill(1959) |
Question 1205112: Suppose 𝑋1, 𝑋2, . . . is a discrete time Markov chain with the set of state spaces state space 𝑆 = {1, 2, 3, 4, 5, 6} and the transition probability matrix as follows:
𝑃 =
[
0 0 0.5 0.5 0 0
0 0 1 0 0 0
0 0 0 0 0.5 0.5
0 0 0 0 1 0
0.5 0.5 0 0 0 0
1 0 0 0 0 0
]
Find:
(a) 𝑃(𝑋3000000 = 2 | 𝑋0 = 1)
(b) 𝑃(𝑋3000001 = 2 | 𝑋0 = 1)
(c) 𝑃(𝑋3000002 = 2 | 𝑋0 = 1)
Click here to see answer by ElectricPavlov(122) |
Question 1207902: Independent random samples of n1 = 18 and n2 = 13 observations were selected from two normal populations with equal variances.
DATA:-
____________________Population (Ignore the lines)
____________________ 1_____2 (Ignore the lines)
Sample Size_________18____13 (Ignore the lines)
Sample Mean________34.6___32.1 (Ignore the lines)
Sample Variance_____4.5___5.9 (Ignore the lines)
(a) Find the rejection region for the test in part (a) for 𝛼 = 0.01. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
t > _______
t < _______
(b) Find the value of the test statistic. (Round your answer to three decimal places.)
t =
(c) Find the approximate p-value for the test.
p-value < 0.010
i) 0.010 < p-value < 0.020
ii) 0.020 < p-value < 0.050
iii) 0.050 < p-value < 0.100
iv) 0.100 < p-value < 0.200
v) p-value < 0.200
Click here to see answer by ElectricPavlov(122) |
Question 1206945: Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 22 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.09 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.96 oz and 12.56 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.15 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.15 oz. Use a 0.025 significance level.
A) Compute the test statistic.
B) What is the P-value?
Click here to see answer by ElectricPavlov(122) |
Question 1207529: Here is a two-way table of counts. The expected counts come second. The data is based on SRS with two categorical variables. Is it safe to use the chai Square test with critical values from the chi-Square distribution?
50: 51.54 36: 31.65 12: 14.99
16: 18.34 13: 11.31 6: 5.36
54: 50.30 25: 31.01 17: 14.69
A. Yes, because all of the observed counts equal five or greater.
B. Yes, because all of the expected counts equal or greater.
C. No because the counts are not whole numbers.
D. Because the sum of the observed counts equals the sum of expected counts.
Click here to see answer by ElectricPavlov(122) |
Question 1204803: During my office hours (12pm to 6pm), an average of 2 students per hour comes in for help. Assuming that the probability of a student coming in is uniform throughout my office hours, what are the odds that on a particular day I would have 6 students come in for help? What is the mean number of students that will come see me on a particular day? Variance? Standard deviation?
Click here to see answer by ElectricPavlov(122) |
Question 1204266: Once a baby is born, an option becomes available to harvest the stem cells of the child from the umbilical cord. This is done at the hospital, in the labour ward. The specimen must be cooled very quickly and maintained at the same temperature for extended periods (often many years). Three competing refrigeration units are tested against one another by the claim that they are able to reduce the temperature of the specimen, in the hospital, to the required level in a minimum amount of time. The refrigeration units are tested at 27 randomly allocated labour wards around the Western Cape. The rate at which the desired temperature is reached (in seconds) is below.
Refrigeration Unit : Temperature rate (in seconds)
Unit 1 : 82; 61; 63; 91; 88; 71; 59; 65; 58; 49
Unit 2 : 67; 58; 72; 71; 54; 79; 44; 60; 77
Unit 3 : 91; 112; 84; 81; 76; 54; 82; 64
Calculate at a 10% level of significance whether there is a significant difference between the mean time until the correct temperature is reached in the three refrigeration units.
Click here to see answer by ElectricPavlov(122) |
Question 1203805: Sometimes it is desirable to assign numerical "code" values to experimental responses that are not basically of numerical type For example in testing the color preferences of experimental subjects suppose that the colors blue, green, and red occur with probabilities 1/4, 1/4, and 1/2, respectively. A different integer value is assigned to each color, and this corresponds to a random variable X that can take on one of these three integer values.
(a) Can f(x) = (1/4)^|x|(1/2)^1-|x| for x = -1, 1, 0 be used as a pdf for this experiment?
(b) Can f(x) = (2 x)(1/2)^2 for x = 0, 1, 2 be used?
(c) Can f(x)=(1-x)/4 for x= -1,0,2 be used?
Click here to see answer by ElectricPavlov(122) |
Question 1204410: The expected number of defective parts produced on an assembly line per shift is 50 with a standard deviation of 8. Use Chebyshev's inequality to find the minimum probability that the number of defective parts on a particular shift will be between 22 and 78. (Round your answer to four decimal places.)
Click here to see answer by ElectricPavlov(122) |
Question 1208818: You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 99% confidence level and a margin of error of 2%. A pilot survey reveals that 8 of the 47 sampled hold two or more jobs. (Use t Distribution Table & z Distribution Table.)
How many in the workforce should be interviewed to meet your requirements? (Round z-score to 2 decimal places. Round up your answer to the next whole number.)
Click here to see answer by ElectricPavlov(122) |
Question 1203976: Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:
Summary
Groups Sample Size Sum Average Variance
Line A 6 250 41.66667 0.266667
Line B 6 260 43.33333 0.666667
Line C 6 249 41.5 0.7
ANOVA
Source of Variation SS df MS F p-value
Between Groups 12.33333 2 6.166667 11.32653 0.001005
Within Groups 8.166667 15 0.544444
Total 20.5 17
Compute 99% confidence intervals that estimate the difference between each pair of means. (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places.) Which pairs of means are statistically different?
Click here to see answer by asinus(45) |
Question 1203801: Let e = (i, j) represent an arbitrary outcome resulting from two rolls of the four-sided die of Example 2.1.1. Tabulate the discrete pdf and sketch the graph of the CDF for the following random variables
(a) Y(e)=i+j.
(b) Z(e)=i-j.
(c) W(e)=(i-j)^2
Click here to see answer by asinus(45) |
Question 1202773: The payouts for the Powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is $1.00.
Divisions Payout Odds. Probability
Five plus Powerball $ 50,000,000 144,407,962 .000000006925
Match 5 250,000 3,560,209 .000000280882
Four plus Powerball 10,000 583,922 .000001712555
Match 4 170 13,575 .000073659399
Three plus Powerball 170 11,927 .000083836351
Match 3 10 291 .003424657534
Two plus Powerball 10 745 .001340482574
One plus Powerball 3 127 .007812500000
Zero plus Powerball 2 69 .014285714286
a. Find the mean and standard deviation of the payout without taking into account the price of the ticket.
b. If the cost of a ticket is taken into account, then the mean is a loss of ________ and the standard deviation is unchanged.
Click here to see answer by asinus(45) |
Question 1202149: A sample of 10 adult men gave the following data on their heights and weights:
Height (inches) X 62 62 63 65 66 67 68 68 70 72
Weight (pounds) Y 120 140 130 150 142 130 135 175 149 168
a) Use a 1% level of significance to test the claim that ρ > 0. Show all steps of your hypothesis test.
b) The predicted weight of a 60 in. tall man (y) would be 122.8, or 123 lbs. Find a 90% confidence interval for men of height 60 inches. Include your interpretation of the confidence interval. Show your formula for E with all important values included.
---
Thank you!
Click here to see answer by asinus(45) |
Question 1207903: Independent random samples of n1 = 18 and n2 = 13 observations were selected from two normal populations with equal variances.
DATA:-
____________________Population (Ignore the lines - it represents space)
____________________ 1_____2 (Ignore the lines - it represents space)
Sample Size_________18____13 (Ignore the lines - it represents space)
Sample Mean________34.6___32.1 (Ignore the lines - it represents space)
Sample Variance_____4.5___5.9 (Ignore the lines - it represents space)
(a) Find the rejection region for the test in part (a) for 𝛼 = 0.01. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
t > _______
t < _______
(b) Find the value of the test statistic. (Round your answer to three decimal places.)
t =
(c) Find the approximate p-value for the test.
p-value < 0.010
i) 0.010 < p-value < 0.020
ii) 0.020 < p-value < 0.050
iii) 0.050 < p-value < 0.100
iv) 0.100 < p-value < 0.200
v) p-value < 0.200
Click here to see answer by asinus(45) |
Question 1208011: Independent random samples of n1 = 18 and n2 = 13 observations were selected from two normal populations with equal variances.
_________________Population (IGNORE THE LINES - represents space)
_________________1_______2 (IGNORE THE LINES - represents space)
Sample Size_____18_______13 (IGNORE THE LINES - represents space)
Sample Mean____34.6______32.1 (IGNORE THE LINES - represents space)
Sample Variance_4.5______5.9 (IGNORE THE LINES - represents space)
(a) Find the rejection region for the test in part (a) for 𝛼 = 0.01. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
t > ________
t < ________
(b) Find the value of the test statistic. (Round your answer to three decimal places.)
t = __________
Click here to see answer by asinus(45) |
Question 1202115: A sample of 10 adult men gave the following data on their heights and weights:
Height (inches) X 62 62 63 65 66 67 68 68 70 72
Weight (pounds) Y 120 140 130 150 142 130 135 175 149 168
a) Use a 1% level of significance to test the claim that ρ > 0. Show all steps of your hypothesis test.
b) The predicted weight of a 60 in. tall man (y) would be 122.8, or 123 lbs. Find a 90% confidence interval for men of height 60 inches. Include your interpretation of the confidence interval. Show your formula for E with all important values included.
---
Thank you!
Click here to see answer by asinus(45) |
Question 1201209: a)Suppose a randomly selected passenger is about to go through the metal detector at LAX.
Consider the following two outcomes: the passenger sets off the metal detector and the passenger does not set off the metal detector. If you are to find the probability of these two outcomes, would you use the classical approach or the relative frequency approach? Explain why.
b) The coach of a college football team thinks there is .75 probability that the team will win the national championship this year. Is this the case of classical, relative frequency or subjective probability? Explain why.
Click here to see answer by asinus(45) |
Question 1205113: In a soccer league consisting of 𝑛 soccer teams, each soccer team plays against every other soccer team twice. against every other soccer team 2 times. Each match awards a certain number of points for a soccer team based on the result that the soccer team gets in the match. match. A win, a draw, and a loss give a soccer team 𝑎, 𝑏, and 𝑐 points respectively in each match; where 𝑎 + 𝑐 > 2𝑏 and 𝑏 > 𝑐. The final ranking of the soccer league will be based on the points earned by the soccer teams after competing against by the soccer teams after competing against each of the other soccer teams twice. The soccer team that earns more points will be ranked higher than the soccer team that earns less points.
than the soccer team with fewer points. If 2 or more football teams achieve the same number of points, then the ranking among them will be randomly drawn. In
the soccer league, a soccer team wishes to be ranked at least𝑘th or higher in the final ranking. or higher in the final ranking of the soccer league. State the minimum points that the soccer team must get in 𝑎, 𝑏, 𝑐, 𝑛, and 𝑘
Click here to see answer by asinus(45) |
Question 1201611: What NCAA college basketball conferences have the higher probability of having a
team play in college basketball’s national championship game? Over the last 20 years,
the Atlantic Coast Conference (ACC) ranks first by having a team in the championship
game 10 times. The South-eastern Conference (SEC) ranks second by having a team in
the championship game 8 times. However, these two conferences have both had teams
in the championship game only one time, when Arkansas (SEC) beat Duke (ACC) 76 - 70 in 1994 (NCAA website, April 2009). Use these data to estimate the following
probabilities.
a) What is the probability the ACC will have a team in the championship game?
b) What is the probability the SEC will have team in the championship game?
c) What is the probability the ACC and SEC will both have teams in the championship
game?
d) What is the probability at least one team from these two conferences will be in the
championship game? That is, what is the probability a team from the ACC or SEC
will play in the championship game?
e) What is the probability that the championship game will not a have team from one
of these two conferences?
Click here to see answer by asinus(45) |
Question 1205111: Cars entering a highway section have an increasing speed during a certain time interval and follow a nonhomogeneous Poisson process with a rate of
𝜆(𝑡) = 18𝑡 per hour. The duration or time spent by cars on the highway section is a uniformly distributed random variable in the interval [2, 4] hours. Assume that there is no interaction between cars and the random times of cars on the toll road are independent. Suppose 𝐴(𝑡) is the number of cars entering the toll road section during [0, 𝑡] and suppose 𝑋(𝑡) is the number of cars in the toll road section at time 𝑡.
Determine
(a) 𝑃(𝐴(2) = 40 | 𝐴(1) = 20)
(b) 𝐸[𝑋(10)]
Click here to see answer by asinus(45) |
Question 1202044: Much has been made of the concept of experimenter bias, which refers to the fact that even the most conscientious experimenters tend to collect data that come out in the desired direction (they see what they want to see). Suppose we use students as experimenters. All the experimenters are told that subjects will be given caffeine before the experiment, but one-half of the experimenters are told that we expect caffeine to lead to good performance and one-half are told that we expect it to lead to poor performance. The dependent variable is the number of simple arithmetic problems the subjects can solve in 2 minutes. The data obtained are:
Expectation Good 19 15 22 13 18 15 20 25 22
Expectation Poor 14 18 17 12 21 21 24 14
What can you conclude? Test the hypothesis at α = 0.05
Click here to see answer by asinus(45) |
Question 1201238: In a resort town during the season, there are n vacationers. Each vacationer has breakfast approximately P1% of the time and dinner P2% of the time at a café. Each time a vacationer chooses a café randomly. There are m cafés in the town. Entrepreneur Feliks wants to set up another one. What is the minimum number of seats needed in this café so that it is not overfilled more than r% of evenings during dinner? What is the probability that such a café will be overfilled during breakfast? Use the Moivre-Laplace theorem. ([n, m, P1, P2, r] = [2105, 7, 58, 52, 8])
Click here to see answer by asinus(45) |
Question 1201173: At a large company banquet for several thousand employees and their families, many of the attendees became ill the next day. The company doctor suspects that the illness may be related to the fish, one of three options for the main course. Because all the dinner guests had to pre-order their meal, the doctor was able to randomly select and contact 80 people that ate the fish, of which 64 people got sick. The doctor also randomly selected (and contacted) 60 people that did not eat the fish, of which 39 people got sick. The doctor also knows that at least 1000 attendees ordered the fish.
a) Is this convincing evidence that the true proportion of all attendees who ate the fish that got sick is more than the true proportion of all attendees who did not eat the fish that got sick?
b) Based on your conclusion in the previous problem, which mistake (a Type I error or a Type II error) could you have made? Interpret the potential error in context.
Click here to see answer by asinus(45) |
Question 1202001: An ornithologist wants to catch a certain pair of birds - a female and a male. The birds are caught one by one until a pair is formed. It is known that in such a bird population, females make up P% of the population. On average, how many birds will the ornithologist have to catch? (P = 33)
Click here to see answer by asinus(45) |
Question 1200870: 5.Summary is obtained from two independent Normal samples
Sample1 Sample2
Sample size 20 40
Sample mean 28 30
Sample standard deviation 8 10
a) Test whether one can assume equal variances.
b) With a suitable test procedure, test for equality of mean
Click here to see answer by asinus(45) |
Question 1207795: You wish to test the following claim (Ha)at a significance level of a=0.004.
You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:
data
54.9
51.5
61.5
66.5
68.2
71.5
76.5
74.9
77.9
91.5
81.5
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Click here to see answer by asinus(45) |
Question 1200772: There are m white balls and 100 - m black balls in an urn. Two players take turns drawing one ball from the urn until the k-th white ball is drawn. What is the probability that the first player will draw the k-th white ball and win the game? (m = 68, k = 5)
Click here to see answer by asinus(45) |
Question 1200769: When admitted to the Chess club, Tomas has to play three games with club members A, B, and win at least two games in a row. The probabilities of Tomas losing against A and B are pA and pB, respectively. The outcomes of the games are independent of each other. Tomas can choose only one opponent order: ABA or BAB. What is the probability of winning in the club in the first and second cases? ([pA, pB] = [0.47, 0.53])
Click here to see answer by asinus(45) |
Question 1200759: Question: Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning.
Blue-chip stocks are safe investments.
Stocks that pay a high rate of interest are safe investments.
Therefore, blue-chip stocks pay a high rate of interest.
response: valid; direct reasoning
valid; indirect reasoning
valid; transitive reasoning
invalid; false chain pattern
invalid; fallacy of the inverse
Click here to see answer by asinus(45) |
Question 1201073: A corporation must appoint a president, chief executive officer (CEO), chief financial officer (CFO) and chief operating officer (COO). It must also appoint a planning committee with six different members. There are 12 qualified candidates, and officers can also serve on the committee.
(i) How many different ways can the officers be appointed?
(ii) What is the probability of randomly selecting the officers and getting the youngest candidate a president?
(iii) How many different ways can the committee be appointed?
(iv) What is the probability of randomly selecting the committee members and getting the six youngest of the qualified candidates?
Click here to see answer by asinus(45) |
Question 1200797: A study of the nicotine contents of a certain brand of cigarette shows that on the
average one cigarette contains 1.52mg of nicotine with a standard deviation of
0.07mg. According to Chebyshev’s theorem, between what values must the
nicotine content be for at least 48/49 of all cigarettes of this brand?
Click here to see answer by GingerAle(43) |
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