A property and casualty insurance company (which provides fire coverage for dwellings) felt that the mean distance from a home to the nearest fire department in rural Alabama was at least 10 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 10 miles due to the increased number of volunteer fire departments. This, they felt, would convince the insurance company to lower its rates. They randomly identify 64 homes and measure the distance to the nearest fire department for each. The resulting sample mean was 8.7 miles. If σ = 3.5 miles, does the sample show sufficient evidence to support the community’s claim? Use the four step process for Hypothesis Testing.

Step 1 – State Hypothesis in context of the problem.

Step 2 – Gather data, check assumptions, and find rejection region using α.

Step 3 – Calculate the appropriate test statistic and p-value.

Step 4 – State conclusion in context of the problem.

Find the maximum value and minimum value in milesTracker. Assign the maximum value to maxMiles, and the minimum value to minMiles. Sample output for the given program:

Min miles: -10
Max miles: 40

Java Code: Remember we can only add to the code. We cant change whats already given. Thank you.

import java.util.Scanner;

public class ArraysKeyValue {
public static void main (String [] args) {
Scanner scnr = new Scanner(System.in);
final int NUM_ROWS = 2;
final int NUM_COLS = 2;
int [][] milesTracker = new int[NUM_ROWS][NUM_COLS];
int i;
int j;
int maxMiles; // Assign with first element in milesTracker before loop
int minMiles; // Assign with first element in milesTracker before loop

for (i = 0; i < milesTracker.length; i++){
for (j = 0; j < milesTracker[i].length; j++){
milesTracker[i][j] = scnr.nextInt();
}
}

/* Answer goes here*/
  
  
System.out.println("Min miles: " + minMiles);
System.out.println("Max miles: " + maxMiles);
}
}

Some people believe that different octane gasoline result in different miles per gallon in a vehicle. The following data is a sample of 11 people which were asked to drive their car only using 10 gallons of gas and record their mileage for each 87 Octane and 92 Octane.

Do the data support that different octanes produce different miles per gallon at the α=0.02α=0.02 level of significance? Note: A normal probability plot of difference in car mileage between Octane 87 and Octane 92 indicates the population could be normal and a boxplot indicated no outliers.

a. Express the null and alternative hypotheses in symbolic form for this claim. Assume μ¯d=μ1−μ2,μd¯=μ1-μ2, where μ1μ1 is the population mean mileage for Octane 87 and μ2μ2 is the mean mileage for Octane 92.

1) H0:μd¯

2) H1:μd¯

b. What is the significance level?

α=

c. What is the test statistic? Round to 3 decimal places.

d. What is the p -value? Round to 5 decimal places.

e. Make a decision.

• Reject the null
• Do not reject the null

f. What is the conclusion?

• There is sufficient evidence to support the claim that different octanes produce different miles per gallon.
• There is not sufficient evidence to support the claim that different octanes produce different miles per gallon.

For data CIR, regress involact on race and interpret the coefficient. Test the hypothesis to determine the claim that homeowners in zip codes with high percent minority are being denied insurance at higher rate than other zip codes. What can regression analysis tell you about the insurance companies claim that the discrepancy is due to greater risks in some zip codes?zip race fire theft age volact involact income
60626 10.0 6.2 29 60.4 5.3 0.0 11744
60640 22.2 9.5 44 76.5 3.1 0.1 9323
60613 19.6 10.5 36 73.5 4.8 1.2 9948
60657 17.3 7.7 37 66.9 5.7 0.5 10656
60614 24.5 8.6 53 81.4 5.9 0.7 9730
60610 54.0 34.1 68 52.6 4.0 0.3 8231
60611 4.9 11.0 75 42.6 7.9 0.0 21480
60625 7.1 6.9 18 78.5 6.9 0.0 11104
60618 5.3 7.3 31 90.1 7.6 0.4 10694
60647 21.5 15.1 25 89.8 3.1 1.1 9631
60622 43.1 29.1 34 82.7 1.3 1.9 7995
60631 1.1 2.2 14 40.2 14.3 0.0 13722
60646 1.0 5.7 11 27.9 12.1 0.0 16250
60656 1.7 2.0 11 7.7 10.9 0.0 13686
60630 1.6 2.5 22 63.8 10.7 0.0 12405
60634 1.5 3.0 17 51.2 13.8 0.0 12198
60641 1.8 5.4 27 85.1 8.9 0.0 11600
60635 1.0 2.2 9 44.4 11.5 0.0 12765
60639 2.5 7.2 29 84.2 8.5 0.2 11084
60651 13.4 15.1 30 89.8 5.2 0.8 10510
60644 59.8 16.5 40 72.7 2.7 0.8 9784
60624 94.4 18.4 32 72.9 1.2 1.8 7342
60612 86.2 36.2 41 63.1 0.8 1.8 6565
60607 50.2 39.7 147 83.0 5.2 0.9 7459
60623 74.2 18.5 22 78.3 1.8 1.9 8014
60608 55.5 23.3 29 79.0 2.1 1.5 8177
60616 62.3 12.2 46 48.0 3.4 0.6 8212
60632 4.4 5.6 23 71.5 8.0 0.3 11230
60609 46.2 21.8 4 73.1 2.6 1.3 8330
60653 99.7 21.6 31 65.0 0.5 0.9 5583
60615 73.5 9.0 39 75.4 2.7 0.4 8564
60638 10.7 3.6 15 20.8 9.1 0.0 12102
60629 1.5 5.0 32 61.8 11.6 0.0 11876
60636 48.8 28.6 27 78.1 4.0 1.4 9742
60621 98.9 17.4 32 68.6 1.7 2.2 7520
60637 90.6 11.3 34 73.4 1.9 0.8 7388
60652 1.4 3.4 17 2.0 12.9 0.0 13842
60620 71.2 11.9 46 57.0 4.8 0.9 11040
60619 94.1 10.5 42 55.9 6.6 0.9 10332
60649 66.1 10.7 43 67.5 3.1 0.4 10908
60617 36.4 10.8 34 58.0 7.8 0.9 11156
60655 1.0 4.8 19 15.2 13.0 0.0 13323
60643 42.5 10.4 25 40.8 10.2 0.5 12960
60628 35.1 15.6 28 57.8 7.5 1.0 11260
60627 47.4 7.0 3 11.4 7.7 0.2 10080
60633 34.0 7.1 23 49.2 11.6 0.3 11428
60645 3.1 4.9 27 46.6 10.9 0.0 13731

For data CIR, regress involact on race and interpret the coefficient. Test the hypothesis to determine the claim that homeowners in zip codes with high percent minority are being denied insurance at higher rate than other zip codes. What can regression analysis tell you about the insurance companies claim that the discrepancy is due to greater risks in some zip codes?zip race fire theft age volact involact income
60626 10.0 6.2 29 60.4 5.3 0.0 11744
60640 22.2 9.5 44 76.5 3.1 0.1 9323
60613 19.6 10.5 36 73.5 4.8 1.2 9948
60657 17.3 7.7 37 66.9 5.7 0.5 10656
60614 24.5 8.6 53 81.4 5.9 0.7 9730
60610 54.0 34.1 68 52.6 4.0 0.3 8231
60611 4.9 11.0 75 42.6 7.9 0.0 21480
60625 7.1 6.9 18 78.5 6.9 0.0 11104
60618 5.3 7.3 31 90.1 7.6 0.4 10694
60647 21.5 15.1 25 89.8 3.1 1.1 9631
60622 43.1 29.1 34 82.7 1.3 1.9 7995
60631 1.1 2.2 14 40.2 14.3 0.0 13722
60646 1.0 5.7 11 27.9 12.1 0.0 16250
60656 1.7 2.0 11 7.7 10.9 0.0 13686
60630 1.6 2.5 22 63.8 10.7 0.0 12405
60634 1.5 3.0 17 51.2 13.8 0.0 12198
60641 1.8 5.4 27 85.1 8.9 0.0 11600
60635 1.0 2.2 9 44.4 11.5 0.0 12765
60639 2.5 7.2 29 84.2 8.5 0.2 11084
60651 13.4 15.1 30 89.8 5.2 0.8 10510
60644 59.8 16.5 40 72.7 2.7 0.8 9784
60624 94.4 18.4 32 72.9 1.2 1.8 7342
60612 86.2 36.2 41 63.1 0.8 1.8 6565
60607 50.2 39.7 147 83.0 5.2 0.9 7459
60623 74.2 18.5 22 78.3 1.8 1.9 8014
60608 55.5 23.3 29 79.0 2.1 1.5 8177
60616 62.3 12.2 46 48.0 3.4 0.6 8212
60632 4.4 5.6 23 71.5 8.0 0.3 11230
60609 46.2 21.8 4 73.1 2.6 1.3 8330
60653 99.7 21.6 31 65.0 0.5 0.9 5583
60615 73.5 9.0 39 75.4 2.7 0.4 8564
60638 10.7 3.6 15 20.8 9.1 0.0 12102
60629 1.5 5.0 32 61.8 11.6 0.0 11876
60636 48.8 28.6 27 78.1 4.0 1.4 9742
60621 98.9 17.4 32 68.6 1.7 2.2 7520
60637 90.6 11.3 34 73.4 1.9 0.8 7388
60652 1.4 3.4 17 2.0 12.9 0.0 13842
60620 71.2 11.9 46 57.0 4.8 0.9 11040
60619 94.1 10.5 42 55.9 6.6 0.9 10332
60649 66.1 10.7 43 67.5 3.1 0.4 10908
60617 36.4 10.8 34 58.0 7.8 0.9 11156
60655 1.0 4.8 19 15.2 13.0 0.0 13323
60643 42.5 10.4 25 40.8 10.2 0.5 12960
60628 35.1 15.6 28 57.8 7.5 1.0 11260
60627 47.4 7.0 3 11.4 7.7 0.2 10080
60633 34.0 7.1 23 49.2 11.6 0.3 11428
60645 3.1 4.9 27 46.6 10.9 0.0 13731

James is a college senior who is majoring in Risk Management and Insurance. He owns a high-mileage 1998 Honda Civic that has a market value of $2,800. The current replacement value of his clothes, television sets, stereo set, cell phone, and other property in a rented apartment totals $9,000. He has a waterbed in his rented apartment that has leaked in the past. An avid runner, James runs 5 miles daily in a nearby public park that has the reputation of being very dangerous because of drug dealers, numerous assaults and muggings, and drive-by shootings. For each of the following risks or loss exposures, identify an appropriate risk management technique that could have been used to deal with the exposure. Explain your answer. (3 questions)

1. Liability lawsuit against James arising out of negligent operation of his car

2. Waterbed leak that causes property damage to the apartment

3. Physical assault on James by gang members who are dealing drugs in the park where he runs

Download the dataset returns.xlsx. This dataset records 83 consecutive monthly returns on the stock of Philip Morris (MO) and on Standard & Poor’s 500 stock index, measured in percent. Investors might be interested to know if the return on MO stock is influenced by the movement of the S&P 500 index. Please be aware that return is defined as new price − old price old price × 100%, so it is always reported as a percentage.

6. Fit a linear regression model for this dataset and verify that the least-squares regression line is ˆy = 0.3537 + 1.1695x. Also record the values of the regression standard error, sample correlation, and coefficient of determination. Interpret the coefficient of determination in context.

7. Calculate a 95% confidence interval for the slope of the regression line. What is the margin of error for this interval? Interpret this interval in context.

8. Perform a hypothesis test to see if there is a linear relationship between the two variables. Be sure to write the null and alternative hypotheses, calculate the test statistic, find the p-value and critical value, and state an appropriate conclusion. Round to 4 decimal places.

9. Calculate a 95% confidence interval for the mean monthly returns on the stock of Philip Morris when the S&P stock index is 3.0. Interpret this interval in context.

10. Calculate a 95% prediction interval for the monthly return on the stock of Philip Morris when the S&P stock index is 3.0. Interpret this interval in context.

Two team (A and B) play a series of baseball games. The team who wins three games of five-game-series wins the series. Consider A has home-field advantage (0.7 means A has probability of winning 0.7 if it plays in its field) and opponent-field disadvantage (0.2 means A has probability of winning 0.2 if it plays in opponents field). If the series start on A team’s field and played alternately between A and B team’s fields, find the probability that series will be completed in four games.

1f. Compare 1a and 1d, and 1b and 1e, explain why the percentage in 1a is much larger than that in 1d and why the value in 1b is much smaller than that in 1e?

1. Suppose that for Edwardsville High School, distances between students’ homes and the high school observe normal distribution with the average distance being 4.76 miles and the standard deviation being 1.74 miles. Express distances and z scores to two decimal places. Write the formula to be used before each calculation.

1a. What percentage of students in the high school live farther than 6.78 miles from the school?

1b. A survey shows that 8% of the students who live closest to the school choose to walk to school. What is the maximum walking distance of these 8% of students? In other words, what is the distance below which these 8% of students live from the school?

1c. Suppose that the school district’s policy allows students living beyond 4.50 miles from the school to take school buses to go to school. There are 3,567 students who enroll in the fall semester, 2006. How many students in the high school are not eligible to take school buses?

1d. Suppose all samples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

1e. Below what value are 8% of sample means of size 12?