For each of the following you should decide
a) What test would you use?
b) Why would you use this test?

1. You wonder if changing the format on a statistics test will change the average mark on the test. You randomly select half the class and give them the standard test. The other half receives the test with the new format. You then compare the marks for each half. In analyzing the data you notice that the group that got the standard test has a normal distribution but the new format has created a bimodal distribution in that half of the class.

2. You wonder which gas station has better service Petro Canada or Shell. Over a 10 day period you ask 30 people to visit the Petro Canada and the Shell station. Each person purchases exactly $10 worth of gas at one station then drives across the road and gets $10 at the other station. You then record the time it takes for each person to be served.

3. You want to see if Rec and Leisure students get summer jobs faster than other university students. You find out from the student placement service that the average university student gets a summer job in 4 weeks with a variance of 3 weeks. The average Rec and Leisure student gets a job in 3.6 weeks with a variance of 4.2 weeks.

Question 1: For each of the following below you should decide
a) What test would you use?
b) Why would you use this test?

1. You wish to test the hypothesis that introverted people earn less money than extroverted people. You sample 27 people from your graduating class and ask them how much money they make and also give them a test to determine how introverted they are. This test of introversion yields a score from 0 to 100 with 0 being not introverted at all (i.e. extroverted) and 100 being very introverted.

2. There are 2 washing machines in your apartment building and you think that the time it takes to wash your clothes varies depending on which machine you use. You decide to test this and spend one afternoon in your laundry room. You record the time it takes to wash one load each time a person does their laundry and end up with the following data. Machine 1 was used 14 times and the mean time for 1 wash was 22.1 minutes with a standard deviation of 2.2 minutes. Machine 2 was used 17 times and took an average of 21.0 minutes per wash with a standard deviation of 1.6 minutes

3. You have developed a new treatment for Alzheimer’s and wish to test it. You give your treatment to 15 patients with suspected Alzheimer’s disease and a placebo to 15 other patients with suspected Alzheimer’s disease. Your treatment is inexpensive, and has few side effects. You give each person a memory test after 3 months of treatment. Scores on this test are based on number of items remembered from a list after a delay of 1 hour.

Answer these questions about the study described here: A group of second graders are being studied to find out the effects of various exercises on their health. Subjects in the study are divided into control and experimental groups. One group is instructed to partake in frequent and intense exercise activities for two weeks. The second group is instructed to maintain their normal routine. Health screenings are performed on the subjects after the two-week period to identify differences. 1. Is this an observational or experimental study? 2. Define the control group. 3. Define the experimental group. 4. What is (are) the independent variable(s)? 5. Suggest a way of measuring the independent variable(s). 6. What is (are) the dependent variable(s)? 7. Suggest a way of measuring the dependent variable(s). 8. List three confounding variables. 9. How could the study on the second graders be designed in order to control for the confounding variables you listed?

Reports suggest that the average credit card debt for recent college graduates is $3000. FedLoan Servicing believes the average debt of graduates is much less than this, so it conducts a study of 50 randomly selected graduates and finds that the average debt is $2975, and the population standard deviation is $1000. Let’s conduct the test based on a Type I error of α=0.05.

USE R AND SHOW CODES!!

3.a. In 1988, 71% of 15-44 year old women who have ever been married have used some form of contraception. What is the probability that, in a sample of 200 women in these childbearing years, fewer than 120 of them have used some form of contraception?

3.b. About 1 percent of women have breast cancer. A cancer screening method can detect 80 percent of genuine cancers with a false alarm rate of 10 percent. What is the probability that women producing a positive test result really have breast cancer?

Please when answering the question, attach a screenshot of the answers and codes from R! Thank you

Taller basketball players have a theoretical shooting advantage because it’s harder to block them. But can a player’s height determine how well they shoot free throws, where there is no defender?

a) Determine the coefficient of determination and interpret its value.

b) What is the equation of the regression line? Keep three decimal places for calculated values.

c) Estimate the percentage of free throws a 200cm tall player will make.

1. Hire-a-Car System rents three types of cars at two different locations. The profit made per day for each car type and company at the two locations is listed below:

The management forecasts the demand per day by car type. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each type of car. The demand forecast for a particular day is 125 rentals for Type 1 cars, 55 rentals for Type 2 cars, and 40 rentals for Type 3 cars. The company has 100 cars in location A and 120 cars in location B.

Use linear programming to determine how many reservations to accept for each car type and how the reservations should be allocated to the different locations. Is the demand for any car type not satisfied? Explain.

Salaries of 47 college graduates who took a statistics course in college have a​ mean, overbar x​, of $65,600. Assuming a standard​ deviation, σ​, of $12,213​, construct a 95​% confidence interval for estimating the population mean μ.

$__ < μ < $ __

A travel association reported the domestic airfare (in dollars) for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years.

(a)

Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period.

H₀: μ_d = 0

H_a: μ_d ≠ 0

H₀: μ_d < 0

H_a: μ_d = 0

H₀: μ_d ≥ 0

H_a: μ_d < 0

H₀: μ_d ≠ 0

H_a: μ_d = 0

H₀: μ_d ≤ 0

H_a: μ_d > 0

Calculate the test statistic. (Use current year airfare − previous year airfare. Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =  

Using a 0.05 level of significance, what is your conclusion?

Reject H₀. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.Reject H₀. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.     Do not reject H₀. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period. Do not reject H₀. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.

(b)

What is the sample mean domestic airfare (in dollars) for business travel for each year?

current $  previous $  

(c)

What is the percentage change in mean airfare for the one-year period? (Round your answer to one decimal place.)

  %

Question 1

    Which of the following statements about the Chi Square statistic is NOT true?

1. Chi Square squares the differences between observed and expected frequencies, thus inflating the true difference.
2. Chi Square is not calculated from observed and expected frequencies.
3. Chi Square is artificially inflated by sample size.
4. Measures of association need to be on standardized scales with a 0 meaning no relationship and 1 meaning a perfect relationship. Chi square can be virtually any positive number.

Question 2

Which of the following Phi statistics would represent the weakest relationship?

1. .02
2. .15
3. .28
4. .37

Question 3

    What statistic tells you the likelihood of drawing a sample with a measure of association at least as strong as the one drawn from a population where that measure of association is zero?

1. Significance Statistic
2. Cramer's V
3. Phi
4. Alpha Level

Question 4

    What is the null hypothesis for the relationship between age and opinions on abortion?

1. There is a relationship between age and opinions on abortion in the sample.
2. There is no relationship between age and opinions on abortion in the population.
3. There is a relationship between age and opinions on abortion in the population.
4. There is a relationship between age and opinions on abortion in the population.

The following results come from two independent random samples taken of two populations.

(a)

What is the point estimate of the difference between the two population means? (Use

x₁ − x₂.)

(b)

Provide a 90% confidence interval for the difference between the two population means. (Use

x₁ − x₂.

Round your answers to two decimal places.)

  to  

(c)

Provide a 95% confidence interval for the difference between the two population means. (Use

x₁ − x₂.

Round your answers to two decimal places.)

If you take this sample and break into 2 samples, one for graduate degrees (MBA and MSE) and one for undergraduate degrees (BA and BSE), would you believe the populations have different GPAs?

1. What test would you perform?
   1. Z-test of a mean
   2. T-test of a mean
   3. T-test of 2 sample means
   4. Chi-square test
2. What is the value of the test statistic?
   1. 2.02
   2. 2.68
   3. 3.06
   4. 3.11
3. What is the p-value?
   1. 0.0074
   2. 0.0280
   3. 0.0373
   4. 0.0746
4. Based on a significance level of 0.05, would you reject or fail to reject and why?
   1. Reject because p < alpha
   2. Reject because p > alpha
   3. Fail to reject because p < alpha
   4. Fail to reject because p > alpha

A random sample of 20 subjects was asked to perform a given task. The time in seconds it took each of them to complete the task is recorded below:

If we assume that the completion times are normally distributed, find a 95% confidence interval for the true mean completion time for this task. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

What is the lower limit of the confidence interval?

What is the upper limit of the confidence interval?

Question 1: A researcher would like to estimate the true mean number of hours adults sleep at night. Suppose that population sleep time is known to follow a Normal distribution with standard deviation as 1.5 hours. The researcher random select 100 people and found the average sleeping hours for the sample of 100 people is 6.5 hours.

1) Use this sample mean to estimate the true population mean of sleep time with 95% confidence. (hint: 95% CI)

2) If the researcher intends to increase the confidence of the estimation to 99%, what is the CI now. Compare the 99% CI with the 95% CI calculated in previous question, what has been changed?

3) If the researcher wants to increase the confidence of estimation to 99% without extend the margin of error, what should this researcher do? (hint: sample size)

4) Reflect on previous questions and the CI formula , what factors can affect the CI and how?