Consider a binary response variable y and an explanatory variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses.

a. Test for the significance of the intercept and the slope coefficients at the 5% level in both models.

b. What is the predicted probability implied by the linear probability model for x = 19 and x = 24? (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

c. What is the predicted probability implied by the logit model for x = 19 and x = 24? (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Beer bottles are filled so that they contain an average of 455 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 6 ml. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected bottle will have less than 452 ml of beer? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 452 ml? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that a randomly selected 12-pack of beer will have a mean amount less than 452 ml? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

A random sample of size n = 152 is taken from a population of size N = 3,300 with mean μ = −71 and variance σ² = 112. [You may find it useful to reference the z table.]

a-1. Is it necessary to apply the finite population correction factor?

• Yes

• No

a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)

b. What is the probability that the sample mean is between −73 and −69? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that the sample mean is greater than −70? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Flip a coin 3 times, what is 1. outcome 2. sample space 3. event(two tails) 4. event space(two tails)

1. Length (in days) of human pregnancies is a normal random variable (X) with mean 266, standard deviation 16.

a. The probability is 95% that a pregnancy will last between what 2 days? (Remember your empirical rule here)

b. What is the probability of a pregnancy lasting longer than 315 days?

2. What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? In other words, what is P(Z < 1.05)?

3. What is the probability that a normal random variable will take a value that is between 1.5 standard deviations below the mean and 2.5 standard deviations above the mean? In other words, what is P(−1.5 < Z < 2.5)?

4. What is the probability that a normal random variable will take a value that is more than 2.55 standard deviations above its mean? In other words, what is P(Z > 2.55)?

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5994 physicians in Colorado showed that 3359 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

Give a brief explanation of the meaning of your answer in the context of this problem.

99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.    

1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.

(c) Is the normal approximation to the binomial justified in this problem? Explain.

No; np > 5 and nq < 5.

Yes; np < 5 and nq < 5.    

No; np < 5 and nq > 5.

Yes; np > 5 and nq > 5.

Wildlife biologists inspect 137 deer taken by hunters and find 22 of them carrying ticks that test positive for Lyme disease.

A) Create a​ 90% confidence interval for the percentage of deer that may carry such ticks.

B) If the scientists want to cut the margin of error in​ half, how many deer must they​ inspect?

C) What concerns do you have about this​ sample?
A. Since females and young deer are usually not​ hunted, this sample may not be representative of all deer.​ Also, since deer ticks are parasites and can easily be spread from one deer to​ another, the ticks may not be distributed evenly throughout the deer population.

B. Since females and young deer are usually not​ hunted, this sample may not be representative of all deer.

C. Since deer ticks are parasites and can easily be spread from one deer to​ another, the ticks may not be distributed evenly throughout the deer population.

D. There are no concerns about this study.

The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. Assume that the population standard deviation is 2.2 gallons. The mean water usage per family was found to be 15.8 gallons per day for a sample of 669 families. Construct the 90% confidence interval for the mean usage of water. Round your answers to one decimal place.

QUESTION 1

1. Joyce works in a toy factory maintaining machines. Machines should inject exactly 500 grams of plastic into a mold to make a toy plane. Joyce wonders if these toy machines might need cleaning, but it's a lot of work taking apart the machines to do a proper job. She grabs planes from 24 different machines at random and weighs them. Her average is 495 grams. She knows there's a standard devation of 10 grams for all machines (Joyce has been doing this for a while). What is Joyce's conclusion as a result of this test? (Check all that apply.) Note the critical z value for 90% confidence is 1.645.

   		Fail to reject the null hypothesis.
   		Reject the null hypothesis at 90% confidence.
   		Reject the null hypothesis at 95% confidence.
   		Reject the null hypothesis at 99% confidence.

QUESTION 2

1. Now suppose Joyce doesn't have population standard deviation (perhaps because these are new machines); she only has her sample standard deviation which is 12. Using the same information, (500 grams average, sample mean of 495, sample size of 24), what are the results of Joyce's analysis? (Check all that apply.) You will need to use one of the tables available on Blackboard (knowing which one is part of the question).

   		Fail to reject the null hypothesis.
   		Reject the null hypothesis at 90% confidence.
   		Reject the null hypothesis at 95% confidence.
   		Reject the null hypothesis at 99% confidence.

The College Board finds that the distribution of students' SAT scores depends on the level of education their parents have. Children of parents who did not finish high school have SAT math scores X with mean 448 and standard deviation 106. Scores Y of children of parents with graduate degrees have mean 562 and standard deviation 101. Perhaps we should standardize to a common scale for equity. Find numbers a, b, c, and d such that a + bX and c + dY both have mean 500 and standard deviation 100. (Round your answers to two decimal places.)

(A) What type of pattern exists in the data?
a. Positive trend, no seasonality
b. Horizontal trend, no seasonality
c. Vertical trend, no seasonality
d. Positive tend, with seasonality
e. Horizontal trend, with seasonality
f. Vertical trend, with seasonality

(B) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.

(C)

(D)Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

(E) Compute the quarterly forecasts for next year based on the model you developed in part (d).
Do not round your interim computations and round your final answer to three decimal places.

(F) Is the model you developed in part (b) or the model you developed in part (d) more effective? If required, round your intermediate calculations and final answer to three decimal places.

1.     Summarize the cost by calculating the mean and standard deviation for each region

2.     Calculate the Standard deviation for all five regions   

3.     Use a bar graph for this data set and show the five averages on the graph

4.     List all the averages and standard deviations of five regions for comparison

Cost due to traffic congestion, per registered vehicle.
               
      City      Cost Traffic
Northeastern cities   Baltimore, MD   530  
       Boston, MA   880  
       Hartford, CT   250  
       New York, NY   1,090  
       Philadelphia, PA   420  
       Pittsburgh, PA   400  
       Washington, DC   1,420  
Midwestern cities   Chicago, IL   570  
       Cincinnati, OH   200  
       Cleveland, OH   140  
       Columbus, OH   230  
       Detroit, MI   530  
       Indianapolis, IN   130  
       Kansas City, MO   160  
       Louisville, KY   190  
       Milwaukee, WI   370  
       Minneapolis-St. Paul, MN   270  
       Oklahoma City, OK   190  
       St. Louis, MO   540  
Southern cities   Atlanta, GA   640  
       Charlotte, NC   390  
       Ft. Lauderdale, FL   290  
       Jacksonville, FL   400  
       Memphis, TN   140  
       Miami, FL      680  
       Nashville, TN   340  
       New Orleans, LA   340  
       Norfolk, VA   390  
       Orlando, FL   420  
       Tampa, FL   310  
Southwestern cities   Albuquerque, NM   210  
       Austin, TX      410  
       Corpus Christi, TX   50  
       Dallas, TX      750  
       Denver, CO   420  
       El Paso, TX   120  
       Fort Worth, TX   420  
       Houston, TX   750  
       Phoenix, AZ   630  
       Salt Lake City, UT   90  
       San Antonio, TX   290  
Western cities   Honolulu, HI   470  
       Los Angeles, CA   980  
       Portland, OR   500  
       Sacramento, CA   280  
       San Bernardino-River, CA   1,320  
       San Diego, CA   480  
       San Francisco-Oakland, CA   930  
       San Jose, CA   960  
       Seattle-Everett, WA   880  

If you select 5 students from your sample where n=60, what is the probability that you will select at least 3 Females? Create a Frequency Distribution Graph to demonstrate your outcome.

Write a response addressing the following prompt: During presidential elections, election forecasters will typically use exit polls to try to predict the outcome of the presidential election. We will often hear that a candidate’s lead is “outside the margin of error” at a 95% confidence level. What does this mean? In your answer, be sure to include the following: Explain what margin of error and confidence intervals are. How does it help us estimate a population parameter? What does it mean when there is a “statistical tie”? Why is it dangerous to make predictions “within the margin of error”?

A research team conducted a study showing that approximately 15% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight

(b) more than two ties are too tight

(c) no tie is too tight

(d) at least 18 ties are not too tight