Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1169144: Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 5%. A mutual-fund rating agency randomly selects 24 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 3.73%. Is there sufficient evidence to conclude that the fund has moderate risk at the a=0.10 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed.
o=0.05
0<0.05
i need to find x to the second power
Click here to see answer by CPhill(1959)   |
Question 1169076: You and your friend are taking the driving test to obtain your driver’s licenses. The
probability for you to pass the test is 0.9 and for your friend it is 0.8. Calculate the
probability that you two make a total of 8 attempts to obtain your licenses.
(if you got your license on the 2nd attempt and your friend got his on 3rd attempt, you
made a total of 5 attempts)
Click here to see answer by CPhill(1959) |
Question 1169056: A researcher claims that the Republican Party is going to win in the next Senate elections especially in Florida State. A statistical data stated that 23% of the voters opted for the Republican Party in the last election. In order to test the claim, an investigator surveyed 80 people and found 22 of them voted for Republican Party in the last election held. Is there enough statistical evidence at α = 0.05 to support the claim of the researcher?
Click here to see answer by CPhill(1959) |
Question 1169044: Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 144 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
Probability that fewer than 37 voted
The probability that fewer than 37 of 144 eligible voters voted is ____.
(Round to four decimal places as needed.)
Click here to see answer by CPhill(1959) |
Question 1169008: A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?
70 84 42 65 41 24 58 63 69 49 61 72 90 91 67
Need to find
Hypothesis test
p-value
Click here to see answer by CPhill(1959) |
Question 1169004: NHTSA new car crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data on new cars, saved in the CRASH file. Crash test dummies were placed in the driver’s seat and front passenger’s seat of a new car model, and the car was steered by
remote control into a head-on collision with a fixed barrier while traveling at 35 miles per hour. Two of the variables measured for each of the 98 new cars in the data set are (1) the severity of the driver’s chest injury and (2) the severity of the passenger’s chest injury. (The more points assigned to the chest injury rating, the more severe the injury is.) The files demonstrated that the mean chest injury rating was significantly higher for drivers than for passengers. A similar study utilized independent random samples of size 18 and yielded the data shown in the table below on the chest injury rating of cars for drivers and passengers.
Chest Injury Rating
Car Driver Passenger Car Driver Passenger
1 42 35 10 36 37
2 42 35 11 36 37
3 34 45 12 43 58
4 34 45 13 40 42
5 45 45 14 43 58
6 40 42 15 37 41
7 42 46 16 37 41
8 43 58 17 44 57
9 45 43 18 42 42
Question: State the null and alternative hypotheses.
Thank you!
Click here to see answer by CPhill(1959) |
Question 1169002: In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3. Answer parts (a)(c) below.
(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 487.
The probability that a randomly selected medical student who took the test had a total score that was less than is 487
(Round to four decimal places as needed.)
(b) Find the probability that a randomly selected medical student who took the test had a total score that was between 500 and 513.
The probability that a randomly selected medical student who took the test had a total score that was between 500 and 513 is
(Round to four decimal places as needed.)
(c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 53`.
The probability that a randomly selected medical student who took the test had a total score that was more than 531 is
(Round to four decimal places as needed.)
Click here to see answer by CPhill(1959) |
Question 1168947: On the planet of Mercury, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.
a. What is the distribution of X?
b. Find the probability that the child spends less than 2.8 hours per day unsupervised.
c. What percent of the children spend over 3.9 hours per day unsupervised. (Round to 2 decimal places)
d. 78% of all children spend at least how many hours per day unsupervised?
Click here to see answer by CPhill(1959) |
Question 1210177: The data for the two variables X and Y are given in the table below:
X: 1.11, 0.00, 0.47, 0.23, 0.14, 0.29, 0.53, 0.61, 0.83, 0.65, 1.05, 0.31
Y: 2.38, 1.03, 1.00, 0.90, 0.93, 0.90, 1.06, 1.16, 1.57, 1.22, 2.18, 0.91
X: 1.35, 0.04, 1.03, 0.64, 0.86, 0.22, 0.30, 1.23, 1.49, 0.48, 1.07, 1.35
Y: 3.32, 0.99, 2.12, 1.21, 1.65, 0.90, 0.91, 2.82, 3.98, 1.01, 2.25, 3.32
Part I
Given that X ~ U(0, θ) (i.e., X is uniformly distributed on [0, θ]), we can use the following estimators for θ:
T₁ = 2X̄, where X̄ is the sample mean.
T₂ = 2m̂, where m̂ is the sample median.
T₃ = 2√3S, where S is the sample standard deviation.
T₄ = max {X₁, X₂, …, Xₙ}, where the maximum value is taken from the sample.
a) Compute the estimates T₁, T₂, T₃, T₄ for θ using the given sample data.
b) Compare the standard errors of the above estimators.
c) Assume that we additionally know that θ = 1 + e, with e ~ Exponential(1) and θ ≤ 2. Use the Bayesian inference technique to find θ and compare the error of this estimator with the ones above.
Part II
d) Calculate the sample correlation coefficient between X and Y.
e) Test the hypothesis "X and Y are correlated".
Part III
We consider the linear regression model:
Y = a + bX + cX² + ε,
where a, b, c are the coefficients and ε is the error term.
f) Find the regression coefficients a, b, c.
g) Construct 95% confidence intervals for a, b, and c.
h) Assume that we use the above regression model to predict Y = y₀ at x₀ = 0.5. Calculate the prediction error and construct the 95% confidence interval for y₀.
Click here to see answer by CPhill(1959) |
Question 1168892: 6. Fred received an exam score of 92 points in a biology class where the average was 89 and the standard deviation was 4. What was his standardized score (z-score)? I got z=o.75 am I correct?
7. Fred received an exam score of 87 points in a criminology class where the average was 83 and the standard deviation was 6. What was his standardized score (z-score)? I got z=0.67
8. Relatively speaking, did Fred (from questions 6 & 7) perform better on his biology or criminology exam? I got Biology am I correct?
9. What type of error has occurred when a researcher falsely rejects the null hypothesis? I got Type 1 error am I correct?
10. A researcher studying gender differences in mental stress collects data from a random sample of men and women. After conducting her analysis, the researcher concludes that there is a significant difference in everyday levels of mental stress between males and females, with women showing higher levels of day to day stress. However, in reality there is no difference in mental stress levels between men and women. What type of error has the researcher committed? Type 1 error am I correct?
11. In order to run a z-test for one sample mean, we must know the ____________ and standard ____________________ of the population with which our sample is being compared. I GOT INFORMATION AND STANDARD DEVIATION
Click here to see answer by ElectricPavlov(122) |
Question 1168872: You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32students. You want to test this claim. You randomly select 18 classes taught by full time faculty and determine the class size of each. The results are listed below. At a=o.01, can you support the university's claim.
35 28 29 33 32 40 26 25 29
28 30 36 33 29 27 30 28 25
Research Question:
I. Hypotheses:
Ho: µ
Hi:µ
IV. Decision:
II. Criteria for Decision:
a =
Decision Rule:
Reject H 0 if p-value <
Ill.Test Statistics:
V. Summary:
Click here to see answer by CPhill(1959) |
Question 1168870: The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. Use the 68-95-99.7 Rule to answer the following questions.
(a) What percentage of pregnancies last between 250 and 282 days?
(b) What percentage of pregnancies last fewer than 250 days?
(c) What percentage of pregnancies last between 266 and 298 days?
(d) What percentage of pregnancies last more than 298 days?
(e) What percentage of pregnancies last between 234 and 282 days?
Click here to see answer by CPhill(1959) |
Question 1168856: a sample of 400 male students is found to have a mean height of 67.47 inches.can it be reasonably regarded as a sample from a large population with mean height 67.39 inches and standard deviation 1.3 inches?test at 5% level of significance
Click here to see answer by CPhill(1959) |
Question 1168843: A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?
70 84 42 65 41 24 58 63 69 49 61 72 90 91 67
Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses?
Need t find
test statstic and p-value
Click here to see answer by CPhill(1959) |
Question 1168842: Listed below are the lead concentrations in ug/g measured in different traditional medicines. Use a 0.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 16 ug/g. Assume that the sample is a simple random sample.
5 125 19.5 22.5 4.5 5.5 10.5 13 8.5 22
Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses?
nned to find test statistic
and p-value
Click here to see answer by CPhill(1959) |
Question 1168840: Park officials make predictions of times to the next eruption of a particular geyser, and collect data for the errors (minutes) in those predictions. The display from technology available below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
need to find
test statitstic
p-vaue
Click here to see answer by ikleyn(52754)  |
Question 1168839: The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 6.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Need to find
test statistic
p-value
Click here to see answer by ikleyn(52754) |
Question 1210185: The data for the two variables X and Y are given in the table below:
X: 1.11, 0.00, 0.47, 0.23, 0.14, 0.29, 0.53, 0.61, 0.83, 0.65, 1.05, 0.31
Y: 2.38, 1.03, 1.00, 0.90, 0.93, 0.90, 1.06, 1.16, 1.57, 1.22, 2.18, 0.91
X: 1.35, 0.04, 1.03, 0.64, 0.86, 0.22, 0.30, 1.23, 1.49, 0.48, 1.07, 1.35
Y: 3.32, 0.99, 2.12, 1.21, 1.65, 0.90, 0.91, 2.82, 3.98, 1.01, 2.25, 3.32
Part I
Given that X ~ U(0, θ) (i.e., X is uniformly distributed on [0, θ]), we can use the following estimators for θ:
T₁ = 2X̄, where X̄ is the sample mean.
T₂ = 2m̂, where m̂ is the sample median.
T₃ = 2√3S, where S is the sample standard deviation.
T₄ = max {X₁, X₂, …, Xₙ}, where the maximum value is taken from the sample.
a) Compute the estimates T₁, T₂, T₃, T₄ for θ using the given sample data.
b) Compare the standard errors of the above estimators.
c) Assume that we additionally know that θ = 1 + e, with e ~ Exponential(1) and θ ≤ 2. Use the Bayesian inference technique to find θ and compare the error of this estimator with the ones above.
Part II
d) Calculate the sample correlation coefficient between X and Y.
e) Test the hypothesis "X and Y are correlated".
Part III
We consider the linear regression model:
Y = a + bX + cX² + ε,
where a, b, c are the coefficients and ε is the error term.
f) Find the regression coefficients a, b, c.
g) Construct 95% confidence intervals for a, b, and c.
h) Assume that we use the above regression model to predict Y = y₀ at x₀ = 0.5. Calculate the prediction error and construct the 95% confidence interval for y₀.
The answer provided by @CPhill is incomplete and incorrect.
Click here to see answer by asinus(45) |
Question 1168838: Consider a drug testing company that provides a test for marijuana usage. Among 311 tested subjects, results from 25 subjects were wrong (either a false positive or a false negative). Use a 0.01 significance level to test the claim that less than 10 percent of the test results are wrong.
Need to find
Hypothesis test
p-value
Click here to see answer by CPhill(1959) |
Question 1168837: Suppose 242 subjects are treated with a drug that is used to treat pain and 51 of them developed nausea. Use a 0.05 significance level to test the claim that more than 20% of users develop nausea.
Need to find hypotheis test
p-value
Click here to see answer by CPhill(1959) |
Question 1168836: Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, among 6083 patients treated with this drug, 159 developed the adverse reaction of nausea. Use a 0.10 significance level to test the claim that 3% of users develop nausea. Does nausea appear to be a problematic adverse reaction?
Need to find hypothesis test
p-value
Click here to see answer by CPhill(1959) |
Question 1168833: In a study of the accuracy of fast food drive-through orders, one restaurant had 31 orders that were not accurate among 356 orders observed. Use a 0.01 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?
Need to find
Hupothesis test
p-value
Click here to see answer by CPhill(1959) |
Question 1168831: In a study of the accuracy of fast food drive-through orders, one restaurant had 31 orders that were not accurate among 356 orders observed. Use a 0.01significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?
Need to find the
Hypothesis test
p-value
Click here to see answer by CPhill(1959) |
Question 1168824: Based on historical data, your manager believes that 30% of the company's orders come from first-time customers. A random sample of 97 orders will be used to estimate the proportion of first-time-customers.
What is the probability that the sample proportion is greater than than 0.2?
Answer = (Enter your answer as a number accurate to 4 decimal places.)
Click here to see answer by CPhill(1959) |
Question 1168822: Based on historical data, your manager believes that 35% of the company's orders come from first-time customers. A random sample of 179 orders will be used to estimate the proportion of first-time-customers.
What is the probability that the sample proportion is less than 0.31?
Answer = (Enter your answer as a number accurate to 4 decimal places.)
Click here to see answer by CPhill(1959) |
Question 1168610: Listed below are speeds (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at 3:30 P.M. on a weekday. Use the sample data to construct 95% confidence interval estimate of the population standard deviation.
62,63,63,56,63,52,61,60,61,69,60,66
Need to find
The confidence interval estimate is mi/h < o < mi/h
(round to one decimal place as needed)
Click here to see answer by CPhill(1959) |
Question 1210187: Five people check identical suitcases before boarding an airplane. At the baggage claim, each person takes one of the five suitcases at random. What is the probability that exactly one person ends up with the wrong suitcase?
Click here to see answer by CPhill(1959) |
Question 1168570: If we roll a die two times, determine whether the following pairs of events are independent or dependent.
Event A is rolling a 3 on the first die. Event B is getting a sum of more than 6 with the two dice?
Click here to see answer by CPhill(1959) |
Question 1168569: In a study of the effect of predictability on stress, subjects were either given a public speaking assignment with an hours advanced notice or they were instructed to give the speech immediately. Stress experienced right before beginning the speech was measured. They collected data from a small sample of 14 people with 7 in each group, and found that the group that was given notice of the speech had a mean stress level of 4.00 while the group who did not have advanced notice had a mean stress level of 7.71. The standard error of the mean difference was .71. Test the hypothesis that giving warning of an upcoming stressful event reduces the stress experienced by individuals.
Question:
1. Statistical Hypotheses H0: µ1 - µ2 = H1: µ1 - µ2 ≠
2. Decision Rule
3. Reject the null hypothesis at the .05 level of significance if t equals or is greater than ___ or if t equals or is less than__ given df = __
4. Calculate the appropriate t test
5. Decision: ____ the null hypothesis at the .05 level of significance because the obtained t of ____ is __ than the critical t of ___
6. How would you interpret your decision?
Click here to see answer by CPhill(1959) |
Question 1210189: In a basketball tournament, there are four teams, and each team plays against every other team exactly twice. (So each team plays six games. Also, each team is equally likely to win a game, and there are no ties.) Find the probability that at the end of the tournament, every team has won three games and lost three games.
Click here to see answer by CPhill(1959) |
Question 1210189: In a basketball tournament, there are four teams, and each team plays against every other team exactly twice. (So each team plays six games. Also, each team is equally likely to win a game, and there are no ties.) Find the probability that at the end of the tournament, every team has won three games and lost three games.
Click here to see answer by ikleyn(52754) |
Question 1168434: Suppose the amount of healing oil used annually by household in Ontario is normally distributed with a mean of 760 litres per household per year and standard deviation of 150 litres of heating oil per household per year
A) what is probability that randomly selected Ontario household uses more than 570 litres of heating oil per household per year ?
B) what is probability that randomly selected Ontario household uses between 680 and 1130 litres per year ?
Click here to see answer by ikleyn(52754) |
Question 1168567: A teacher expected students to take about 20 mins on their online exam. She noticed that a lot of her students were taking less time and she is wondering if there is a systematic difference or if what she is seeing is just due to chance. Did her class of 48 students differ significantly from her typical average of 20 mins?
Question:
1. Statistical Hypotheses?
2. reject the null hypothesis at the .05 level of significance if t ≥ __
or t ≤ __ given __ df.
3. what is your decision regarding whether she should reject or accept the null hypothesis.
4. How do you interpret your decision?
Click here to see answer by CPhill(1959) |
Question 1168534: Suppose SAT Writing scores are normally distributed with a mean of 489 and a standard deviation of 112. A university plans to award scholarships to students whose scores are in the top 4%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.
Click here to see answer by CPhill(1959) |
Question 1168489: Scientific research on popular beverages consisted of 60 studies that were fully sponsored by the food industry, and 40 studies that were conducted with no corporate ties. Of those that were fully sponsored by the food industry, 15 % of the participants found the products unfavorable, 23 % were neutral, and 62 % found the products favorable. Of those that had no industry funding, 38 % found the products unfavorable, 15 % were neutral, and 47 % found the products favorable.
a)What is the probability that a participant selected at random found the products favorable?
b)If a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry?
c)If a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?
Click here to see answer by CPhill(1959) |
Question 1168481: Urn A has 2 white and 13 red balls. Urn B has 14 white and 6 red balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed heads?
Click here to see answer by CPhill(1959) |
Question 1168466: During the last 50 years, the consumption of eggs in the United States has decreased by 19%. Fifty years ago, the average consumption was 307 eggs per person per year. What is the average consumption of eggs today? (Round your answer to the nearest whole number.)
Click here to see answer by CPhill(1959) |
Question 1168411: suppose that a brand of light bulb lasts on a average of 2100 hours with a standard deviation of 100 hours. The values also approximate the normal distribution. Estimate the range of the number of hours that will include middle of 40% of the distribution
Click here to see answer by CPhill(1959) |
Question 1168409: 73% of all Americans live in cities with population greater than 100,000 people. If 35 Americans are randomly selected, find the probability that
a. Exactly 26 of them live in cities with population greater than 100,000 people.
b. At most 26 of them live in cities with population greater than 100,000 people.
c. At least 25 of them live in cities with population greater than 100,000 people.
d. Between 21 and 25 (including 21 and 25) of them live in cities with population greater than 100,000 people.
Click here to see answer by CPhill(1959) |
Question 1168408: 64% of all violent felons in the prison system are repeat offenders. If 48 violent felons are randomly selected, find the probability that
a. Exactly 28 of them are repeat offenders.
b. At most 30 of them are repeat offenders.
c. At least 32 of them are repeat offenders.
d. Between 28 and 34 (including 28 and 34) of them are repeat offenders.
Click here to see answer by CPhill(1959) |
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