1. 1000 used car tires are being evaluated by a major insurance company. The quality of the tiers are based on the depth of the treads and years in use. The results from 1000 tires are summarized as the following:

Let A denote the event that a tire is new (less than 2 years old), and let B denote the tire has low depth for treads (less than 3 mm). Determine the number of castings in

1. Put in writing what A∩ B means.
2. Find A∩ B
3. Find A∪ B¢
4. What is the probability that a randomly selected tire is not new with high treads depth?
5. What is the probability that a randomly selected tire is not new with low treads depth?
6. If a selected tire was found to be new, find the probability that it is with high treads depth.
7. Find P(A | B)

Test the claim that the mean GPA of night students is smaller than 3.2 at the .025 significance level.

Based on a sample of 75 people, the sample mean GPA was 3.18 with a standard deviation of 0.06

The test statistic is (to 3 decimals)

The critical value is (to 3 decimals)

The University of Pittsburgh Medical (UPMS) School grades each class in the following manner:

All students whose score is plus or minus two standard deviations from the mean course score receive a grade of “Pass.”

Students whose score is above two standard deviations from the course mean receive a grade of “Pass with Distinction.”

And, students whose score is below two standard deviations from the course mean receive a grade of “Fail.” Course scores are always assumed to be normally distributed.

Approximately what percentage of medical students in each class receives a “Pass with Distinction”?

Grades on a standardized test are known to have a mean of 500 for students in the US. The test is administered to 600 randomly selected students in Florida. In this subsample, the mean is 508, and the standard deviation is 75

i. Construct a 95% confidence interval for the average test score for students in Florida.

ii. Is there statistically significant evidence that students in Florida perform differently from other students in the US?

iii. Another 500 students are selected at random from Florida. They are given a 3 hour preparation course before the test is administered. Their average test score is 514, with a standard deviation of 15. Construct a 95% confidence interval. Is there statistically significant evidence that the preparation course helped? What conditions must be met in order for the results to have a causal interpretation?

Dr. Lillian​ Fok, a New Orleans​ psychologist, specializes in treating patients who are agoraphobic​ (i.e., afraid to leave their​ homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same​ year.                                                                                                                                          

The simple linear regression equation that shows the best relationship between the number of patients and year is ​(round your responses to three decimal​ places):

ModifyingAbove y with carety ​=??????​+??????x where

ModifyingAbove y with carety ​= Dependent Variable and x​ = Independent Variable.

Using linear regression​, the number of patients Dr. Fok will see in year 11​=????? patients​ (round your response to two decimal​ places).

Using linear regression​, the number of patients Dr. Fok will see in year 12​=???? patients ​(round your response to two decimal​ places).

The coefficient of determination for the linear regression model is 0.8621 This shows that there is a (strong) OR (not so strong) relationship between the​ "Number of​ Patients" and​ "Year."

Perfect Properties have collected sales data from property sales in the northern suburbs of Cape Town for the past month. In the table below you are supplied with the selling price (SP) of the house in Rand, the size of the plot in m² (P) as well as the size of the house, also in m² (H). They are interested in understanding which of these two factors influence the selling price.

Use the data in the sheet named “Perfect” and answer the following questions:

1. Decide which linear regression model (with size of plot (P) or size of house (H) or both as independent variable) is the better model in explaining the behaviour of selling prices (SP) and motivate your selection.

The remaining answers must be based on the model that you have selected.

2. What is the total variation in “Selling Price” that is explained by the independent variable(s) that you have selected?
3. Is the overall regression model statistically significant? Test at the 5% level of significance using the model that you have selected in a. For this test formulate the appropriate null and alternative hypothesis, determine the region of acceptance, use the appropriate test statistic and draw the statistical and management conclusions.
4. Write down the linear regression equation in algebraic format using SP for Selling price, P for plot size and H for the size of the house.
5. Compute the expected Selling price for a house that stands on a plot of 1500 m² and has a house that covers 245 m².

Compute the 95% confidence interval of the mean expense for a house that stands on a plot of 1500 m² and has a house that covers 245 m².

Give a detailed example of using a weighted mean. 1a. In your example, how might the weighted mean be a better average than another measure of center like the simple mean? 2. Fill in the second column of the table with any numbers you want. This column will represent number of students who had a certain score on a test. Score N (weight) 60 70 80 90  Calculate Weighted Mean for the score on this test.

A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 18 coughs per minute.

(a) Let r = number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution of r. Coughs are a common occurrence. It is reasonable to assume the events are independent. Coughs are a common occurrence. It is reasonable to assume the events are dependent. Coughs are a rare occurrence. It is reasonable to assume the events are independent. Coughs are a rare occurrence. It is reasonable to assume the events are dependent.

(b) Find the probability of seven or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.)

(c) Find the probability of at least eight coughs (in a large auditorium) in a 28-second period. (Use 4 decimal places.)

1. Give a Real-life example of inferential statistics that will clearly identify your target population; how you would plan on acquiring a random representative sample; and then how you would use this sample to make inferences regarding your target population using this sample.

2. Give an example of a Discrete Variable and an example of a Continuous Variable. Can you also provide your reasoning by Answer the following questions:

Can your variable only be described using whole numbers? If so, it is a numerical discrete variable.

Can your variable only be described using the real number line? In other words, it falls on a continuum. If so, it is a numerical continuous variable.

Stock prices: Following are the closing prices of a particular stock for each trading day in May and June of a recent year.

(a) Find the mean and median price in May. Round the answers to at least two decimal places.

(b) Find the mean and median price in June. Round the answers to at least two decimal places.

(c) Does there appear to be a substantial difference in price between May and June, or are the prices about the same?

a)Describe what each one of the assumptions of the model consists of in an ANOVA and explain the typical way in which these assumptions are verified.

b)What are the graphical methods to determine the difference of means?

Beer: The following table presents the number of active breweries for samples of states located east and west of the Mississippi River.

a) Find the mean and median number of breweries for states east of the Mississippi. Round the answers to at least one decimal place.

(b) Find the mean and median number of breweries for states west of the Mississippi. Round the answers to at least one decimal place.

(c) The sample of western states happens to include California. Remove California from the sample of western states, and compute the mean and median for the remaining western states. Round the answers to at least one decimal place.

House prices: The following table presents prices, in thousands of dollars, of single-family homes for 20 of the 25 largest metropolitan areas in the United States for the third quarter of 2012 and the third quarter of 2013.

Source: National Realtors Association

(a) Find the mean and median price for 2012. Round the answers to at least two decimal places.

(b) Find the mean and median price for 2013. Round the answers to at least two decimal places.

(c) In general, house prices increased from 2012 to 2013. Which increased more, the mean or the median?

An Analyst wants to know if there was a significance difference in the average of hours worked in a week from 2000 (Group 1) to 2004 (Group 2). He gathers all the data from the General Social Survey, and lists the following summary statistics from the sampling.

Source: General Social Survey (sda.berkeley.edu )

What is the correct null hypothesis?

Ho: mu2004-mu2000 < 0

Ho: mu2004-mu2000 does not equal 0

Ho: mu2000-mu2004 > 0

Ho: mu2004-mu2000 = 0

1. A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯ x = 64 x ¯ = 64 hours with a standard deviation of s = 5.6 s = 5.6 hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 98% level of confidence. What sample size should you gather to achieve a 0.5 hour margin of error? He would need to sample bacteria.

2. For a confidence level of 98% with a sample size of 26, find the critical t value. Critical Value = (round answer to 3 decimal places)

3. Assume that a sample is used to estimate a population mean μμ. Find the 80% confidence interval for a sample of size 31 with a mean of 85.9 and a standard deviation of 6.3. Enter your answer accurate to one decimal place. I am 80% confident that the mean μμ is between (blank) and (blank)

4. Assume that a sample is used to estimate a population mean μμ. Find the 95% confidence interval for a sample of size 34 with a mean of 81.3 and a standard deviation of 16.8. Enter your answer accurate to one decimal place.
I am 95% confident that the mean μμ is between (blank) and (blank)