Stats FINAL

suppose we have the regression equation 1/y=12.98-3.61√(x). make a prediction for y when x = 3.8. round to 2 decimal places

.17

suppose 12% of the us population his left-handed. if we take a random sample of 100 Americans, what is the probability more than 15% of our sample will be left handed?

.1788

suppose the number of buses arriving at a stop follows a poisson process with an average. of 6 perhaps. You get to the stop at 4:15. What is the probability you are waiting at 4:30?

.2231

The probability that sam parks in a no-parking zone and gets a parking ticket is. .06, and the probability sam cannot find a legal parking. spot and had to park in a no parking zone is .20. On Tuesday, sam. arrives at school and has to park in a no parking zone. What is the probability he will get a ticket?

.3 or 30%

suppose the proportion of OSU students that live on campus is .22. you take a random sample of 46 students. you get a sample proportion that is unusually high. in. fact, your simply proportion is at the 94t percentile of all possible sample proportions. what is your sample proportion?(2 decimal places)

.31

suppose you are interested in testing Ho: mu=12 vs Ha: mu≠12. suppose sigma is 6, n is 100, x-bar, is 11.5 what is the p-value?

.4047

suppose the number of hours of sleep a person gets follows a Unif(7,9) distribution. What is the probability a randomly selected night of sleep lies within one standard deviation of the mean? round to 2 decimal places

.58

suppose birthdays are equally likely to happen on. any of the 365 days of the. year (ignore leap years). In a randomly chosen group of 30. students, what is the probability that at least 2 students share a birthday?

.71 or 71%

suppose the chance that a randomly chosen person is left handed is .08. Assuming independent, what is. the probability that in a group of 3 randomly chosen students none of them are left handed?

.7787 or 78%

suppose 30% of students have an iPhone and 70% have an android. if 80% of iPhone users and 90% of android users say they play game son their phones, what is the overall percentage of students who play. games on their phones?

.87 or 87%

suppose you would life to estimate the proportion of samples that meet quality control guidelines. if you want the margin of error to at most .04 with 99% confidence, how. many sample of beer should you take?

1041

Suppose you are conducting a poll to estimate the proportion of OSU students that would gamble on college athletics if it was legal to do so. You plan on producing a 90% confidence interval and want your margin of error to be at most 5%. How many students should you sample?

271

suppose you are interested in estimating g the average commute time of OSU students who drive to campus, and you want your margin of error to be no more than 2 minutes with 90% confidence. If the standard deviation of the commute times is 7 minutes, how many students must you sample?

34

the number of typing errors o a page follows a poisson process with an average of 0.8 per page. What. is the probability that there is a least one error in a 5 page document? round to 3 decimal places.

0.982

what is the critical value for an 80% confidence interval (round to 2 decimal places)

1.28

A. test has four multiple choice questions with four answer choices each and four true - false questions. suppose you guess on all problems. let x be the total number of problems you answer correctly. E(x) = 4(.25) + 4(.5)=3. what is the var(x)?

1.75

how many standard deviations away from the mean must you go to capture 95% of the area under the normal curve?

1.96

suppose heights of male students at OSU are normally distributed with a standard deviation of 3 inches. If a student who is 76 inches tall is at the 93rd percentile, what is the average height of OSU male students? round to 2 decimal places.

71.56

Suppose 4 of the tenure track faculty mentioned earlier are cross listed in the department of mathematic, and you want your committee to include to exactly one of them, how many way could this be done?

840

suppose everything else is held constant, which of the following would cause a confidence interval to get wider

increasing the value of sigma

suppose you for a regression of y on x. based on the diagnostic plots you determine the original model doesn't fit very well. you try a transformation and fir a regression of log(y) on log(x). if the value of r^2 increases significantly but. the diagnostic plots still don't seem to indicate the assumptions are met, which. model should you use

neither

you calculate a 95% confidence interval for the true length in inches of "foot-long" sandwiches to be (11.15, 12.05). if a consumer group claims that these foot-long sandwiches are less than a foot on average, does your interval support their claim?

no, it does not support their claim

suppose we have a random sample from he Unif(0,theta) distribution. What is the MOM estimator?

2(x-bar)

you want to test Ho: p= .4 vs Ha: p≠.4. If there are 70 successes out of 150 in your sample, what is the p-value of this test?

.095

suppose a battery manufacturer produces batteries that last an average of 10 hours with a standard deviation of 2 hours from a normal distribution under testing conditions. what is the probability that in a sample of 25 the average battery life is at least 11 hours

.0062

you wish to test Ho: p=.9 vs Ha: p<.9. if alpha =.01 and n =225, find the type 2 error probability if the true value of p is .8

.0228

In a month with 31 days, it raininess on 7 days and ws cold on 12. If it was both rainy and cold on 3 days, how many days were not cold and raining. (i.e. dry and warm)

15

suppose there is a 10% chance of getting a prize in a cereal box. if you buy boxes until you collect 5. prizes, what is the standard deviation of the total number of boxes you will n need to buy? round to 2 decimal places.

21.21

suppose a 95% confidence interval for µ (mu) with sigma unknown based on a sample size 12 is (8.78, 15.24). what is the upper bound of the 95% prediction interval for µ (mu)? round to 2 decimals

23.66

suppose a 95% confidence interval for mu base don a sample of size 20 is (8.78, 15.24). what is the upper bound of the 95% prediction interval for µ (mu)? round to 2 decimals

26.81

suppose the variance of a $1 bet on a casino game is 4.5. what is the variance of the same game if you bet $10?

450

suppose you want to predict students' weight using heigh, shoe size, and wing span, if you have 50. student sin your sample, what is the correct number of denominator degrees of freedom to use for the overall f test.

46

the amount t of time a man has to wait in line for the restroom at a concert follows an exponential distribution with mean 3 minutes. The amount of time a woman has to wait same blah blah is 4 minutes. A man and woman both go to the rest room at the same time. Assuming independence, what is the standard deviation of the difference. in waiting times for man and woman?

5.0

suppose 1.34% of the items produces by a particular assembly line are defective. How many times would be expected to be produced until you get 7 defective items? round to 2 decimals

522.39

suppose I want to construct confidence intervals for the true mean weight of students given certain values of their height. which interval would be wider: one for a student who is 5'8" or 6'4"

6'4"

suppose you are testing the hypothesis: Ho: mu=60 vs Ha: mu>60. if n = 40, sigma = 12, and alpha = 0.05, what is the smallest value of x bar that will cause you to reject the null? round to 2 decimal places

63.12

suppose X~Exp(2) and Y~Exp(3). If X and Y are independent, what. is the joint pdf of X and Y?

6e^(-2x-3y)

suppose you planned on taking a sample size of 100 to estimate a population proportion but you margin of error was too high. if you wanted the margin of error to be a third of was you originally got, how many people would you need to sample?

900

suppose you are testing Ho: mu=24.8 vs. Ha: mu>24.8. You find a 90% confidence interval for mu to be (25.6, 26.2) what should your conclusion be?

At alpha = .05, reject

Which of the following could be a correct set of hypotheses for a test?

H0:μ=.5, Ha:μ≠.5

A factory has two assembly lines (A and B) each day it. randomly. tests a certain number of parts. if the parts pass inspection, they are going on in the assembly process, but if they don't pass inspection they are labeled defective and put aside for further testing. A worker. picks up a random art. from a.the group set aside for further testing. What is the probability the part came from line A?

P(A | Defective)

Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds that can lay waiting in soil for years before sprouting. A farmer wants to estimate the average number of seeds produced by velvetleaf plants. They use a random sample of plants in one cornfield to construct a 95% confidence interval of (968, 2142). Which of the following is a true statement about that interval?

The margin of error for this interval is 587.

Which of the following statements about the t and z distributions is FALSE?

The t distribution should be used instead of the z distribution when the population standard deviation is known.

Multiplying the sample size by 9 reduces the margin of error by a factor of 3.

True

suppose you are interested in testing Ho: mu=12 vs Ha: mu≠12. suppose sigma is 6, n is 100, x-bar, is 11.5. If your conclusion is correct, what type of error did you make?

Type 2 or II

You are conducting a hypothesis test with the following hypotheses: H0:μ=μ0, Ha:μ≠μ0 Based on a sample of size 12, you get a test statistic of t=2.2 and you make a decision based on a significance level of α=.05. Suppose the true mean was actually larger than μ0. Which type of error, if any, did you commit?

Type II error

suppose you are taking 3 classes (referred to as 1, 2, and 3). Let A(i) be the event {get an A in class i}. Describe the following event: A(1) n [A(2) u A(3)]

You get an A in class 1 and in either class 2 or 3

If A and B are mutually exclusive events w non zero probabilities, they are independent

always false

For a continuous random variable X, the values of the pdf f(x) are between 0 and 1

false

Holding other values constant, increasing the point estimate increases the width of the interval.

false

You calculate a t-interval for a population mean. After doing so, you realize you should have done a z-interval instead. When you calculate the correct z interval, it will have a larger margin of error than the incorrect t interval.

false

two random variable that are uncorrelated must also be independent

false

which could be true

the correlation between weight and reading level at and elementary school is .76

An unbiased estimator can have a larger MSE than a biased estimator of the same parameter.

true

Holding other values constant, decreasing the confidence level decreases the width of the interval.

true

If the MLE of a parameter θ is 3p^, the MLE of θ2 must be (3p^)2 .

true

if we find the x-value that maximizes the likelihood function, that value will also maximize the natural log of the likelihood function

true

bases on a sample of 30 students, you calculate a 95% confidence interval for the true average GPA of 3470 students to be (2.84, 3.26). Which is a correct interpretation.

we are 95% confident that the average GPA of all 3470 students is between 2.84 and 3.26

Suppose you are testing H0:μ=100, Ha:μ>100. Which of the following would lead to the test with highest Type II error probability?

α=.01,n=20,μ=105