A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed.

Find the predicted midterm score when the homework 3 score is 19.5. Do not round until the end, then round answer to 2 decimal places.

1. Roll a pair of dice (one is red and the other is green). Let A be the event that the red die is 4 or 5. Let B be the event that the green die is 1 Let C be the event that the dice sum is 7 or 8.

1. Calculate P(A), P(B), P(C)
2. Calculate P(A|C), P(A|B)
3. Are the events A and C independent?

2. Suppose box 1 has four black marbles and two white marbles, and box 2 has two black marbles and five marbles. If you picked one marble from one of the two boxes at random, what it the probability that you picked from box 1 given that the marble you picked is black?

3. A raffle has 5000 tickets with the following prizes: 1 ticket has $2000 prize, 10 tickets have $200 prize, and 20 tickets have $50 prize and 500 tickets have a $20 prize. If to buy a ticket costs $15, and X is the random variable that measures net profit:

1. Calculate the pdf table of X
2. Calculate E(X), Var(X)

4. If a fair coin is flipped 120 times, what is the probability that:

1. The number of heads is more than 70
2. The number of heads between 50 and 70?

5. According to a study, 21.1% of 507 female college students were on a diet at the time of the study.

a) Construct a 99% confidence interval for the true proportion of all female students who were on a diet at the time of this study.

b) Explain what this interval means.

c) Is it reasonable to think that only 17% of college women are on a diet?

6. A used car dealer says that the mean price of a 2008 Honda CR-V is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05?

A police department is interested in learning if men or women do better as a result of their training course. They administer a skills test to 60 newly trained officers: 30 males and 30 females. Use the data below to establish hypotheses and test them using a chi-square test. State the decision with regard to whether the H₀ is ultimately rejected or retained.

21. Complete a simple linear regression on the following data from a random survey of a random sample of free throws made out of 100:

Age (in years)          # of Free throws made (out of 100)

20                               30

22                               36

26                               28

28                               20

33                               25

33                               15

38                               10

42                               25

49                               8

54                               15

55                               22

55                               18

57                               35

60                               12

Provide the equation of the linear regression line (3 pts):
Y = a + bX

Sum of x is 572

Sum of y is 299

Mean of x is 40.8571

Mean of y is 21.3571

Sum of squares is 2575.7143

Sum of products is -669.2857
Provide the coefficient of correlation (2 pts):
How many would free throws would you expect a 42 year old to make (2 pts):
What is the residual for the 42 year old we sampled (2 pts):

Based on a poll, 80% of airline passengers slept or rested during a long flight. Let the random variable x represents the number of airline passengers among the selected six who slept or rested.
A. Construct a table describing the probability distribution and the R Syntax. (2 pts.)
B. Find the probability that at least 2 of the 6 passengers who slept or rested. (2 pts.)
C. Find the mean and standard deviation for the numbers of passengers who slept or rested. (2 pts.)
D. Determine whether 4 is a significantly high number of passengers who slept or rested in a group of 6. Explain. (3 pts.)

Use R:

x P(x)   
0
1
2
3
4
5
6

7. A researcher found that there is an increase in undergraduate students doing part- time jobs to partially support their expenses. It is assumed that 55% of UWindsor students do part time jobs in this current year. The researcher randomly selected 150 UWindsor students and checked whether they work part-time jobs. Answer the following based on this data:

   1. Find the probability that more than 90 students of these 150 selected said that they do part-time jobs.

   2. Find the probability that less than 80 students of these 150 selected said that they do part-time jobs.

1. For the following data:

1. Find the regression equation for predicting Y from X (Provide your work).
2. Use the regression equation to find a predicted Y for each X.
3. Find the difference between the actual Y value and the predicted Y value for each     individual, square the differences, and add the squared values to obtain SS_residual.
4. Calculate the Pearson correlation for these data. Use r² and SSy to compute SS_residual. You should obtain the same value as in part c.
5. Now use SPSS to determine the regression equation, r, r², and SS_residual. (Provide the SPSS output tables.)

The following data contains the characteristics of 30 motorcycles that will be analyzed using a Regression model. You will study the relationship between a motorcycles' engine power (measured in horsepower) and the motorcycles' weight (measured in pounds).

Power (cf): 145 215 165 85 225 87 175 210 158 86 150 150 76 170 208 150 215 225 220 153 175 130 140 165 180 150 190 110 150 86

Weight (lb): 4082 4735 3693 2310 4951 2672 4464 4382 4363 2220 4135 4096 2065 4654 4633 4464 4615 4425 4354 4129 5140 3504 3449 4209 4955 4997 3850 2962 3761 2226

Declare:

a) Explanatory variable:

b) Response variable:

c) Make a scatter diagram. Describe the axes and scales for each axis.

d) What can you say about the strength, direction, and shape? Answer this subjectively (do not calculate the correlation).

e) Assuming that the scatter diagram above is linear with r2 = 0.7142182. Determine the slope and intercept of the regression line. (use the r program to calculate Sweight, Spower.

f) Write the modeled regression line.

g) Interpret the slope

h) What would be the engine power of a car if its weight were 2.5 tons? h.

i) Plot the regression line on the scatter plot

j) Interpret r. agrees with what was thought in point c

k) Interpret r2

how do you calculate 95% confidence interval using population variance

1. A professor hypothesizes that students who earn a C or better in her class spend more time outside of class studying than students who receive a D or F. She collects the following data from two samples of students. What does she conclude?

Number of hours studying per week for C or better students:
8, 4, 4, 2, 1, 5, 3, 2, 3

Number of hours studying per week for D or F students:
6, 2, 1, 0, 3, 2, 1

1. Null hypothesis:
2. Alternative hypothesis:
3. Statistical test (be specific!):
4. Significance level: alpha = .05
5. degrees of freedom:
6. Critical region (t-value):
7. Calculated t (show your work):
8. Decision:

Is there a relationship between body fat and resting rate. Test at alpha =.05 test the significance of the relationship between body fat and resting rate using table I or the traditional five step method.

The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.7% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same-sex couples should have the right to legal marital status.

Construct the probability distribution function (PDF). (Round your probabilities to five decimal places.)

1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. About 68% of all pregnancies last between

a. 250 and 282 days          b. 234 and 298 days           c. 218 and 314 days      d. 250 and 266 days

2. The distribution of actual weights of chocolate bars produced by a certain machine is approximately Normal with mean 8.2 ounces and standard deviation of 0.1 ounces. What proportion of chocolate bars weigh under 8 ounces?

a. 13.5%       b. 34%        c. 16%       d. 2.5%

3. Sixteen weighings of a small object on a sensitive scale result in 5.15 grams 4 times, 5.35 grams 4 times, 5.20 grams, 4 times and 5.30 grams 4 times, 16 total. If the standard deviation σ of weighings on this scale is .8 grams, what is an approximate 95% confidence interval for the true weight of the object?

1. 5.25 ±.4         b. 5.25 ±.2        c. 5.25 ±.8       d. 5.20 ±.2

4. A survey of 900 gun-owners who frequent a popular shooting range in Texas had a nearly 100% response rate. If only 18% of the respondents thought more laws on gun control should be enacted, the conclusion that less than 20% of people in the region support more gun laws would certainly be dubious due to which of the following?

a. large standard deviation of samples of size 900       b. nonresponse from the sample

c. sampling bias of respondents       d. small sample size

5. Scores on a test for 8^th graders range from 0 to 500. In a SRS of 400 students, the mean score is 335 and the standard deviation is 70. The standard deviation of the sampling distribution of x̅₄₀₀ is what?

1. 70/335        b. 400/70       c. 70/20         d. 335/20

6.The weights of a sample of 400 2-year-olds in Kentucky yields x̅₄₀₀ is 21.2 pounds with a standard deviation of σ = 3 pounds. What is a 95% confidence interval for the weight of all two-year-olds in Kentucky?
a. 18.2-21.5 pounds     b. 15.2-27.2 pounds        c. 21.185-22.015 pounds     d. 20.9-21.5 pounds

7.When finding confidence intervals, the interval is smaller if

    a.sample size and standard deviation are bigger    b.sample size and standard deviation are smaller   

c.sample size is bigger, but the standard deviation is smaller   d.sample size is smaller, but standard deviation is bigger.   

8. If the birth weights of the babies born annually in a hospital is Normal with a mean of 5 pounds 10 ounces and a standard deviation of 5 ounces, what percentage of babies are born weighing less than 5 pounds? (No table needed.)

a. 13.5%       b. 2.5%       c. 16%        d. .3%

9. What percent of the babies born weigh between 5 pounds and 5 pound 5 ounces? (Again no table.)

a. 13.5%       b. 47.5%       c. 16%        d. 34%

10. Of the 40 babies born during the first weeks of next month, how many are likely to be under five pounds?

a. 4      b. 2      c. 6     d. 1    

11.) A random sample of 1,600 adults in a certain country shows that 72% have smart phones. What is a 80% confidence interval for the percentage of adults having smart phones in this country?

1. 72%±1.85%     b. 72%±1.44%     c.72%±2.24%     d.72%±1.11%

12.If 48% of the 400 voters sampled voted for candidate A over candidate B, what is a 95% confidence for p hat, the estimate for the percentage candidate p that A would receive?

1. 48%±2.5%      b. 48%±5%     48%±10%     d. 48%±1%

13.Twenty-five randomly selected students are asked how many times a month they eat pizza. The average for this sample is x̅₂₅= 11.75 times,but the population mean of all college students is claimed to be μ = 10.60 times. If the null hypothesis is H₀ is μ = 10.60 times and the standard deviation σ = 5 times, should the null hypothesis be rejected at the 5% level of significance? (No table needed)

1. Yes       b.   No      c. Not enough information      

14. Is the distribution of incomes in the US described by a normal distribution with μ equal to the mean income?

1. Yes    b. No    c. Not enough information

15. The weights of baby orangutans has standard deviation 4 pounds. How large a sample of baby orangutans is necessary for the 95% margin of error to be .5 pounds?

a. 144      b. 324      c. 256   d. 900

16. A car manufacturer says their cars average 26 miles per gallon of gas at 65 miles per hour a standard deviation of σ = 2 miles per gallon.. A Consumer group tested 100 such cars and found the average x̅₁₀₀ to be 25.4 miles per gallon. Is this sufficiently small to reject the null hypothesis H₀: μ = 26 miles per gallon? (No table needed.)

a. Yes     b. No     c. Not enough information.

17. What is the probability that z, the standard normal distribution, is less than 1.75 standard deviations below the mean of zero?

a. 5%      b. 4%      c. 6%      d. 7.4%

18. If two random samples of the heights of adult males in New York are taken, one of 400, the other of 900 people, which one would likely have the larger range from shortest to tallest?

a. the 400 person sample      b. the 900 person sample    c. they’d be equal

19. The p-value of a test of the null hypothesis is 3.5%. This means

a. the hypothesis is true with probability 3.5% or possibly less than 3.5%     b. the alternative hypothesis is true with probability 3.5% or possibly less     c. 3.5% is the probability of finding the observed or more extreme results when the null hypothesis (H ₀) is true     d. None of the above

20. One of the main reasons to be interested in the regression line of y on x is that

a. one can use it to predict y-values from different x-values     b. one can determine the standard deviation of y    

c. one can determine from it the values of the quartiles of x and y.

There are three types of balls in a box: 5 red, 3 blue and 2 green. You draw 3 balls at once (without replacement) from this box and record: Y1=the # of red balls, Y2=the # of blue balls that you drew. Find the joint probability distribution of Y1, Y2, by first writing the possible values for y1, y2 in rows and columns and then filling in the probabilities within this table. Then check that the sum of the entries in the table equals 1.

Given the following distribution, is it a Binomial distribution or approximately a Binomial distribution ? Please justify your answer (prove or disprove) .

X   0 1    2   3   4

P(X) 0.240 0.412 0.265 0.076 0.008