1. You have a number of variables -- a response variable and some proposed predictors. A correlation matrix may help to give an idea of the strength of the linear relationships present. For the purposes of regression analysis, what would be desirable in terms of … a) …the observed correlation between each proposed predictor and the response variable? (2) b) …the observed correlations among the predictors themselves?

(2) 2. Explain the fact that, over the course of a year, the value of r for the DOW adjusted closing value and the S&P500 adjusted closing value is about 0.98 or higher.

(3) 3. Reconcile these observations: In a regression output, the p-value of the F-test is 2.36 E-06, while the value of R2 is 0.21. (3)

4. What causes the problem of multicollinearity? (2)

5. Interpretation of a regression coefficient: Suppose that in a SLR model, annual salary (in thousands of dollars) is estimated as a function of years of education. With explicit reference to the variable units, interpret the value b1 = 3.42. (3)//15

We must show our work.

1. A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 80% confidence interval for the population mean. (Hint: Confidence Interval for a Population mean with population standard deviation (σ) known)

A​ gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the​ gender-selection technique,

862862

births consisted of

448448

baby girls and

414414

baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly

448448

girls in

862862

births.

b. Find the probability of getting

448448

or more girls in

862862

births. If boys and girls are equally​ likely, is

448448

girls in

862862

births unusually​ high?

c. Which probability is relevant for trying to determine whether the technique is​ effective: the result from part​ (a) or the result from part​ (b)?

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let r.v. X represent the number of correct responses on the exam.

1. (a). Specify the probability distribution of X.

2. (b. What is your expected number of correct responses?

3. (c). What are the values of the variance and standard deviation of X?

4. (d). What is the probability that you will get exactly the expected number of correct responses?

The numbers of online applications from simple random samples of college applications for 2003 and for the 2009 were taken. In 2003, out of 312 applications, 97 of them were completed online. In 2009, out of 316 applications, 78 of them were completed online. Test the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003 at the .10 significance level.

Claim: Select an answer u 1 ≤ u 2 u 1 = u 2 p 1 < p 2 u 1 < u 2 p 1 ≤ p 2 p 1≠p 2 u 1 > u 2 p 1 = p 2 u 1≠u 2 u 1 ≥ u 2 p 1 ≥ p 2 p 1 > p 2  which corresponds to Select an answer H1: u 1 > u 2 H0: u 1 ≤ u 2 H1: u 1 < u 2 H0: p 1 = p 2 H1: p 1 < p 2 H1: p 1 > p 2 H1: u 1≠u 2 H0: p 1 ≤ p 2 H1: p 1≠p 2 H0: p 1≠p 2

Opposite: Select an answer u 1 = u 2 p 1 > p 2 u 1 < u 2 p 1 ≤ p 2 p 1≠p 2 u 1 ≥ u 2 u 1 ≤ u 2 u 1 > u 2 p 1 ≥ p 2 p 1 = p 2 u 1≠u 2 p 1 < p 2  which corresponds to Select an answer H1: u 1 <= u 2 H0: u 1 > u 2 H1: u 1 ≥ u 2 H0: u 1≠u 2 H1: u 1 = u 2 H0: p 1 = p 2 H1: p 1 > p 2 H0: p 1≠p 2 H0: p 1 ≤ p 2 H1: p 1≠p 2 H1: p 1 < p 2

The test is: Select an answer /right-tailed / two-tailed / left-tailed

The test statistic is: z = Select an answer 1.79 / 1.95 / 1.47 / 2.28 / 2.05  (to 2 decimals)

Based on this we: Fail to reject the null hypothesis / Accept the null hypothesis / Reject the null hypothesis / Cannot determine anything

Conclusion There Select an answer ( does / does not ) appear to be enough evidence to support the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003.

The critical value is: z a/ 2= ±± Select an answer / 1.64 / 1.44 / 1.64 / 1.28 / 1.15  (to 2 decimals)

33) Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.)

(b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.)

A noted psychic was tested for extrasensory perception. The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime. How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence?

An experiment is picking a card from a fair deck. a.) What is the probability of picking a Jack given that the card is a face card? b.) What is the probability of picking a heart given that the card is a three? c.) What is the probability of picking a red card given that the card is an ace? d.) Are the events Jack and face card independent events? Why or why not? e.) Are the events red card and ace independent events? Why or why not?

7. Circus

A traveling circus has found that its average attendance per performance is 6000 people with a

standard deviation of 1500. Assume that attendance is normally distributed.

a)

Suppose that a town asks the circus to come, but the only available site in town holds a

maximum of 8000 people. What is the probability that this site will reach capacity?

b)

If the circus loses money on 20% of its performances, what attendance must it have to

break even for a performance?

For the data below construct a 95% confidence interval for the population mean.

53.4 51.6 48.0 49.8 52.8 51.8 48.8 43.4 48.2 51.8 54.6 53.8 54.6 49.6 47.2

The president of Amalgamated Retailers International, Sam Peterson, has asked for your assistance in studying the market penetration for the company’s new cell phone. You are asked to determine if the market share is equal to the company’s claim of 35%. You obtain a random sample of potential customers from the area. The sample indicates that 258 out of a total sample of 800 indicate they will purchase from Amalgamated

[a] Using a probability of error , test the hypothesis that the market share equals the company’s claim of 35% versus the hypothesis that the market share is not equal to the company’s claim.

[b] Using a probability of error , test the hypothesis that the market share equals the company’s claim of 35% versus the hypothesis that the market share is less than the company’s claim.

Please Include:

1. The problem statement
2. Assumptions
3. The null and alternate hypothesis statements
4. The significance level
5. The test statistic (as an equation)
6. Decision rules
7. The calculated value of the test statistic
8. The p-value
9. Interpret the results of the test.

A professor has a class with four recitation sections. Each section has 16 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?). At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance. However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.

First, run an ANOVA with this data and fill in the summary table. (Report P-values accurate to 4 decimal places and all other values accurate to 3 decimal places.

To follow-up, the professor decides to use the Tukey-Kramer method to test all possible pairwise contrasts.

What is the Q critical value for the Tukey-Kramer critical range (alpha=0.01)?
Use the website link in your notes (http://davidmlane.com/hyperstat/sr_table.html) to locate the Q critical value to 4 decimal places.
Q =

Using the critical value above, compute the critical range and then determine which pairwise comparisons are statistically significant?

• group 1 vs. group 2
• group 1 vs. group 3
• group 1 vs. group 4
• group 2 vs. group 3
• group 2 vs. group 4
• group 3 vs. group 4
• none of the groups are statistically significantly different

Census data for a city indicate that 29.0​% of the​ under-18 population is​ white, 26.2​% ​black, 33.2​% Latino, 9.5​% ​Asian, and 2.1​% other ethnicities. The city points out that of 25,577 police​ officers, 64.8​% are​ white,14.5​% ​black, 19.1​% ​Latino, 1.4​% ​Asian, and the remaining are other ethnicities. Do the police officers reflect the ethnic composition of the​ city's youth? Complete parts a through e below.

A) What is the appropriate test?

B) What is the null and alternative hypothesis?

C) What is the chi squared test statistic

D) what is the p value

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 220 customers on the number of hours cars are parked and the amount they are charged.

According to actuarial tables, life spans in the United States are approximately normally distributed with a mean of about 75 years and a standard deviation of about 16 years.

1) Find the probability that a randomly selected person lives between 60 less than 90 years.

2) Find the probability that a randomly selected person lives less than 50 years or more than 100 years.

3) Find the probability that a randomly selected person lives exactly 75 years.

4) What age is considered to be the 99th percentile?

5) What age is considered to be in the 10th percentile?