The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a 95% prediction interval for y, the number of days absent, given x = 95 degrees and y = 0.449x - 30.27

a. (9.957, 14.813)

b. (11.378, 13.392)

c. (4.321, 6.913)

d. (3.176, 5.341)

Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. A researcher is interested in the effects of herbicide formulation on spray atomization. The researcher believes a normal distribution with mean 1050 µm and standard deviation 150 µm is a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle.

(a) What is the probability that the size of a single droplet is less than 1380 µm? Greater than 1000 µm? (Round your answers to four decimal places.)

(b) What is the probability that the size of a single droplet is between 1000 and 1380 µm? (Round your answer to four decimal places.)


(c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.)

The smallest 2% of droplets are those smaller than ___ µm in size.

(d) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1380 µm? (Round your answer to four decimal places.)

A researcher was interested in the effects of different study methods on learning, among a class of children. Following one of three methods, 6 students were divided into groups.

1. Using manual computation, perform the appropriate hypothesis test at α = 0.01

Why is this an example of spurious correlation? How do you know? Do not use the same example given from another student. Make sure you read your classmates’ posts before submitting your example.

My example... Number of tigers or elephants in the zoo increases with increasing number of libraries/adult day care center in the city. Can you help me choose which variables are better - Elephants & adult day care, Elephants & libraries. Tiger & Adult day care or Tigers and LIbraries.

Can you explain further - How can i explain - what is the correlation between these 2 variables?

THnak you.

A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 5 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician.

There is a tradeoff between the cost of eroneously discarding a good lot, and the cost of warranty claims if a bad lot is sold. The next few problems refer to this scenario.

(Continues previous problem.) Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 97%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 5 defective chips, and that bad lots contain exactly 20 defective chips.

Problem 16

(Continues previous problem.) The expected number of lots the manufacturer must make to get one good lot that is not rejected by the test is (Q22)

Problem 17

(Continues previous problem.) With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is (Q23)

The table below lists a random sample of 53 speeding tickets on I-25 in Colorado.

(Note: PLease enter your answer as a decimal number , NO FRACTIONS)
a) If a random ticket was selected, what would be the probability that the driver was female?


b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit?
c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female?
d) If a random ticket was selected, what would be the probability that the driver was a male?
e) If a random ticket was selected, what would be the probability that the driver is a female and driving 10-20 mph over the limit?
f) If a random ticket was selected, what would be the probability that the driver is a female or driving 0-10 mph over the limit?

B. The Wilson family was one of the first to come to the U.S. They had 8 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson family had:

at least 7 girls?

at most 2 girls?

1. You wish to test the following claim (Ha) at a significance level of α=0.05.

      Ho:p1=p2
      Ha:p1>p2

You obtain 83% successes in a sample of size n1=305 from the first population. You obtain 78.7% successes in a sample of size n2=315 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

2.  You wish to test the following claim (Ha) at a significance level of α=0.002.

      Ho:μ1=μ2
      Ha:μ1≠μ2

You obtain the following two samples of data.

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? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

1. Give a 95% confidence interval, for μ1−μ2μ1-μ2 given the following information.

n1=30, ¯x1=2.94, s1=0.34
n2=45, ¯x2=2.71, s2=0.53

_____±______ Use Technology Rounded to 2 decimal places.

2. You wish to test the following claim (HaHa) at a significance level of α=0.002. For the context of this problem, μd=PostTest−PreTestμd=PostTest-PreTest where the first data set represents a pre-test and the second data set represents a post-test. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your μ1 and μ2 are so that the differences are computed correctly.)

      Ho:μd=0
      Ha:μd≠0
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?
p-value = (Report answer accurate to 4 decimal places.)

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age and movie preference are not independent.
H₁: Age and movie preference are not independent.

H₀: Age and movie preference are not independent.
H₁: Age and movie preference are independent.    

H₀: Age and movie preference are independent.
H₁: Age and movie preference are not independent.

H₀: Age and movie preference are independent.
H₁: Age and movie preference are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

chi-square

binomial    

uniform

Student's t

normal

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age of young adult and movie preference are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.

For the 2 × 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas.

3 −3 2 3

For row player R:

r1 =

r2 =

For column player C:

c1 =

c2=

Find the value v of the game for row player R.

v =

The chart below lists the sales in thousands of dollars based on the advertising budget for that quarter. The regression equation is Y' = 4.073 + 0.8351X. What is the correlation coefficient?

Multiple Choice

• 0.775

• 0.844

• 0.926

• 1.00

1. You have been hired by a company as a Statistical Consultant, for the purpose of determining whether there is a significant difference in the number of units produced by workers on Mondays and Fridays at their factory. The following table indicate the number of units produced by three groups of eight workers randomly sampled from each of the relevant days.

1. Using manual computation, perform the appropriate hypothesis test at α = 0.05

2. You perform a simple experiment to determine whether the consumption of two units of alcohol has a significant impact upon ability to play computer games. Two samples, each of ten game players, are randomly chosen for the experiment. Subjects in both groups are asked to play a computer game for ten minutes, and the final score of each game player is recorded. The first group play the game being sober, while the second group play the game immediately after consuming two units of alcohol. The results obtained are given in the following table:

                      Score

2. Perform an appropriate hypothesis test at the 5% significance level to determine whether consumption of two units of alcohol has a significant impact upon ability to play computer games, as measured by the final scores obtained by game players. Show all calculations, both manual, and using MS Excel.

After getting trounced by your little brother in a children’s game, you suspect the die he gave you to roll may be unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die’s fairness?

a) If the die is fair, how many times would you expect each face to show?

b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence?

c) State your hypotheses.

d) Check the conditions. Is the counted data conditions met? (Yes or No)

is the randomization condition met? (Yes or No)

Is the expected cell frequency condition met (Yes or No)

e) How many degrees of freedom are there?

f) Find and the P-value. (Round to 4 decimal places)

g) State your conclusion. Assume that 0.05 is a reasonable significance level.

Face   Count
1   14
2   8
3   7
4   9
5   8
6   14

The table below lists maintenance cost vs. the age of cars for a sample of seven cars. The goal was determine if there was a correlation between the age of a car and the cost to maintain it. The least squares regression equation describing the maintenance costs (Y′) vs. the age of the car (X) was determined to be

Y' = −4.75 + 2.8929X

What is the standard error of estimate?

Multiple Choice

• 6.621

• 2.573

• 5.754

• 3.864

In correlation analysis, the independent variable is

Multiple Choice

• the variable that is scaled on the vertical axis.

• the variable that is being predicted or estimated.

• a variable that provides the basis for estimation. It is the predictor variable.

• The independent variable is the variable that provides the basis for estimation. It is the predictor variable. The independent variable is the variable that the dependent variable depends on.