Studies show that 10% of the population is left-handed. In a study with 186 students, only 16 were left-handed. Does this suggest that left-handed students are underrepresented in this study? Use α = 0.1.

Use the following information for Problems 31-33. (You could verify your answers in SPSS, but I would like to see your hand calculations)

Subject           Test X   Test Y

   1                      10          10

   2                      6             8

   3                      6             9

   4                      5             4

   5                      6             10

6                      7 11

7                      9 10

8                      7 9

31. Compute the following values.

(a) r (X,Y) = _________

(b) Using the result from (a) compute S_Y.X = ___________________

(c) Interpret your result to part (b)

32. (a) Using the data above, determine the regression equation to predict Test Y performance

        from the Test X performance.

Regression equation: __________________________

(b) Carefully construct a scatter plot using grid paper and label the regression line. Make sure to LABEL your axes. Insert a copy of your plot in the space provided below. (2 points)

(c) Interpret the slope of the regression line. (1 point)

33. Using the regression equation from the previous problem,

a) What score on Test Y would you predict for someone who scored 5 on Test X?

_________________

            b) How much predictive error is there for the Subject who scored 5 on Test X?

            ________________

As part of a dietary – instruction program, ten 25 – 34-year-old males adopted a vegetarian diet for 1 month. While on the diet, the average daily intake of linoleic acid was 13 g with standard deviation of 4 g. If the average daily intake among 25 – 34-year-old males in the general population is 15 g, then using a significance level of 0.05, test the hypothesis that the intake of linoleic acid in this group is lower than that of the general population. Make sure to state your null and alternative hypotheses, test – statistic, conclusion (technical and descriptive).

b) Using the information from part a, suppose we are uncertain what effect a vegetarian diet will have on the level linoleic – acid intake. Make sure to state your null and alternative hypotheses, test – statistic, conclusion (technical and descriptive).

a) a manuscript contains 1000 pages. After proofreading, the editor found 10 typos. What is the probability that there is no more than 3 typos in a given page.

b) an urn contains 10 white balls, 15 blue balls and 25 red balls. You pick 10 balls at random from the urn. What is the probability that you will not get any red ball.

To study if high cholesterol levels are more common among men than among women, a sample of 244 men and a sample of 232 women were randomly selected. The cholesterol levels were measured and 74 men and 48 women had elevated levels. At α=0.05, can it be concluded that men are more susceptible to having higher levels of cholesterol?

Renal Disease:
The presence of bacteria in a urine sample (bacteriuria) is sometimes associated with symptoms of kidney disease in women. Suppose a determination of bacteriuria has been made over a large population of women at one point in time and 5% of those sampled are positive for bacteriuria.

1. If a sample size of 5 is selected from this population, what is the probability that 1 or more women are positive for bacteriuria?

2. Suppose 100 women from this population are sampled. What is the probability that 3 or more of them are positive for bacteriuria?
One interesting phenomenon of bacteriuria is that there is a “turnover”; that is, if bacteriuria is measured on the same woman at two different points in time, the results are not necessarily the same. Assume that 20% of all women who are bacteriuric at time 0 are again bacteriuric at time 1 (1 year later), whereas only 4.2% of women who were not bacteriuric at time 0 are bacteriuric at time 1. Let X be the random variable representing the number of bacteriuric events over the two time periods for 1 woman and still assume that the probability that a woman will be positive for bacteriuria at any one exam is 5%.

3. what is the probability distribution of X?

4. what is the mean of X?

5. what is the variance of X?

14-57. The Olson Brothers Organic Milk Company recently studied a random sample of 30 of its distributors and found the correlation between sales and advertising dollars to be 0.67.

A. Is there a significant linear relationship between sales and advertising? If so, is it fair to conclude that advertising causes sales to increase?

B. If a regression model were developed using sales as the dependent variable and advertising as the independent variable, determine the proportion of the variation in sales that would be explained by its relationship to advertising. Discuss what this says about the usefulness of using advertising to predict sales.

Suppose that 60% of college students eat pizza weekly. Answer the following questions if you have a random sample of 50 college students. What is the probability that exactly 29 eat pizza weekly? What is the probability that 35 or fewer eat pizza weekly? What is the probability that more than 32 eat pizza weekly?

In a survey of delinquent peers, a small sample of adolescents is asked to rate the overall delinquency of their closest friends on a scale of 1 to 10. Later, the same survey asks the respondents to self-report their delinquency rating on the same scale. The data for twelve subjects are as follows (high scores signify high levels of delinquency):                                               

Compute the Pearson's r and test the significance of the obtained correlation (use α .05) using Table H of Appendix C.

In its latest press release, Pill International announced that they are working on a new drug that would stunt the deterioration of brain cells in Alzheimer's patients. If successful, the drug could prolong the life of patients and allow them to retain their basic mobility.

The R&D team is currently testing the drug, which comes in the form of a digestible tablet, for its ability to be dissolved and absorbed in the bloodstream. Based on their latest experiments, they have learned that there is a relationship between the amount of time that the tablet's powder spends in the tray dryer and the amount of time it takes to get dissolved (Y). As a member of this research team, you have been asked to establish the relationship between the two variables and to predict potential dissolution times based on the time spent in the dryer.

The following data represent the level of health and the level of education for a random sample of 1630 residents.

Excellent Good Fair Poor
Not a H.S. graduate 114 184 106 126
H.S. graduate 75 120 82 94
Some college 110 154 102 107
Bachelor Degree or higher 121 156 85 133

A. Calculate the Chi Square test statistic (Round to three decimal places)

B. Give the P Value (Round to three decimal places)

C. Make a proper conclusion

Reject Ho. There is sufficient evidence that education and health are dependent.

Fail to reject Ho. There is sufficient evidence that education and health are dependent.

Reject Ho. There is not sufficient evidence that education and health are dependent.

Fail to reject Ho. There is not sufficient evidence that education and health are dependent.

Student Debt – Vermont: You take a random sample of 31 college students in the state of Vermont and find the mean debt is $25,000 with a standard deviation of $2,700. We want to construct a 90% confidence interval for the mean debt for all Vermont college students.

(a) What is the point estimate for the mean debt of all Vermont college students?
$
(b) What is the critical value of t for a 90% confidence interval? Use the value from the t-table.

(c) What is the margin of error for a 90% confidence interval? Round your answer to the nearest whole dollar.
$
(d) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar.
(  ,  )

(e) Interpret the confidence interval.

A We expect that 90% of all Vermont college students have a debt that's in the interval.

B We are 90% confident that the mean student debt of all Vermont college students is in the interval.

C We are confident that 90% of all Vermont college students have a debt that's in the interval.

D We are 10% confident that the mean student debt of Vermont college students is in the interval.

(f) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval?

A Because the sample size is greater than or equal to 30.Because the sample size is greater than or equal to 15.   

B Because the margin of error is positive.Because the margin of error is less than or equal 30.

C Because the margin of error is positive.

D Because the margin of error is less than or equal 30.

A local car dealer closes on Sundays at 6:00 pm. He counts the number

of cars available at that time. If there are two or less, order enough to

raise the level to six. Cars are delivered at night and are available when

the exhibition hall opens at 9:00 a.m. on Monday morning. Let Pd (x) be

the probability that the demand during the week is equal to x: Suppose that:

Pd (0) = 0.2 ,Pd (1) = 0.5 ,Pd (2) = 0.2 ,Pd (3) = 0.1

If there is more demand than cars during the week than those available at the

start of it, the excess demand is wasted and the distributor ends the week with

zero cars available. Define a markov chain where states are numbers of cars

available on Monday morning at 9:00 am. Find the transition matrix.

A simple random sample of size n is drawn. The sample​ mean, x ​, is found to be 19.5​, and the sample standard​ deviation, s, is found to be 4.6.

a) Construct a 95% Confidence interval about μ if the sample size n, is 35

(Use ascending order to round to two decimal places as needed

lower bound= Upper bound=

b) Construct a 95% Confidence interval about μ if the sample size n, is 61

lower bound= Upper bound =

(a). How does increasing the level of confidence affect the size of the margin of​ error, E?

A.The margin of error increases.

B.The margin of error decreases.

C.The margin of error does not change

d) If the sample size is

Construct a 99% Confidence interval about μ if the sample size n, is 35

lower bound= Upper bound =

Compare the results to those obtained in part​ (a). How does increasing the level of confidence affect the size of the margin of​ error, E?

A. The margin of error increases.

B.The margin of error decreases.

C.The margin of error does not change.

3. If the sample size is 18 what conditions must be satisfied to compute the confidence​ interval?

A.The sample size must be large and the sample should not have any outliers.

B.The sample data must come from a population that is normally distributed with no outliers.

C.The sample must come from a population that is normally distributed and the sample size must be large.

A class has 40 students.

Thirty students are prepared for the exam, • Ten students are unprepared.

The professor writes an exam with 10 questions, some are hard and some are easy.

• 7 questions are easy. Based on past experience, the professor knows that:

– Prepared students have a 90% chance of answering easy questions correctly

– Unprepared students have a 50% chance of answering easy questions correctly.

• 3 questions are hard. Based on past experience, the professor knows that:

– Prepared students have a 50% chance of answering hard questions correctly

– Unprepared students have a 10% chance of answering hard questions correctly

• Each student’s performance on each question is independent of their performance on other questions.

(a) Find the probability that a prepared student answers all 10 questions correctly.

(b) What is the probability that at least one of the 30 prepared students answers all 10 questions correctly. Assume that each student’s score is independent of every other student.

(c) Let P be the number of questions answered correctly by a randomly chosen prepared student, and let U be the number answered correctly by a randomly chosen unprepared student. Find E[P] and E[U]