Scenario A: You are a Watch Commander in a large metropolitan police agency. Recently, vehicular burglaries have increase substantially in one of the patrol beats under your command. The Captain thinks a saturation patrol strategy would reduce vehicular burglaries. This patrol strategy involves assigning a large number of patrol resources into the beat during times when vehicular burglaries are likely to occur. The theory behind this is that an increased police presence will deter would be burglars. You have been asked to conduct a study to see if a saturation patrol strategy will reduce vehicular burglaries in this patrol beat. Your alternative hypothesis is; An increase of patrol person hours (measured in hours) in the affected beat will reduce vehicular burglaries (measured in the number of incidents).

1. What is the independent variable in the above hypothesis?

2. What is the level of measurement for the independent variable”?

3. What is the dependent variable in the above hypothesis?

4. What is the level of measurement for the dependent variable?

5. What type (association or difference) of hypothesis is the above hypothesis?

Exhibit: Checking Accounts.

A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $300 with a standard deviation of $56. A random sample of 200 checking accounts is selected. You are interested in calculating the following probabilities below.

For all answers below, do not round intermediate steps if any and round your final solution to 4 decimal places.

(1)Assuming that the population of the checking account balances is normally distributed, what is the probability that a randomly selected account has a balance of more than $305?

(2)What is the probability that the mean balance for the selected sample is above $295?

(3)What is the probability that the mean balance for the selected sample is between $302 and $304?

Another one:

A biology class with 114 students recently had an exam. The mean exam score was 82 and the standard deviation of the exam score was 12.

(1)What is the probability that a random sample of 37 exams has an average score below 84?

I need to prove this with some sort of counting...

Suppose there are some number of people in a room and we need need to consider all possible pairwise combinations of those people to compare their birthdays and look for matches.

An Auditor for a government agency is assigned the task ofevaluating reimbursement for office visits to physicians paid byMedicare. The audit is conducted on a sample of 75 of thereimbursements with the follwing results: In 12 of the office visits, an incorrect amount ofreimbursement was provided. The Amount of reimbursement was mean = $93.70 andS=$34.55 a) At the 0.05 level of significance, is there evidence thatthe mean reimbursement is less than $100? b)At the 0.05 level of significance, is there evidence thatthe proportion of incorrect reimbursements in the population isgreater than 0.10? c) Discuss the underlying assumptions of the test used in(a) d) What is yur answer to (a) if the sample mean equals$90? e) What is your answer to (b) if 15 office visits hadincorrect reimbursements?  

The data shows process completion times in hours of a manufacturing plant prior to and after a scheduled routine maintenance operation:

A.) Evaluate the assumption of normality of the datasets

B.) State and test the hypothesis of equal variance in the test populations

C.) State and test the hypothesis that the maintenance operation has any effect on the processing time

The superintendent of the Middletown school district wants to know which of the districts three schools has the lowest rate of parent satisfaction. He distributes a survey to 1,000 parents in each district which asks if the parent is satisfied with their child’s school, and all of these parents respond. Here are the results school

a. Percentage the table in a way that best answers the superintendent’s question

b. Calculate the percentage point difference between the rate of satisfaction at school A and school B, between the rate of satisfaction at school A and school C, and between the rate of satisfaction at school B and school C. Explain what these numbers mean in English.

c. Calculate the chi square value of this table

d. Are the differences shown in this table statistically significant at the 95% level?

e. Based on what you found in (b) and (d), and using your own judgement, how would you answer the superintendent’s question?

1. A sample of the test scores from Mr. D’s old stats class is given below:

84, 67, 85, 82, 99, 78, 88, 94, 82, 90, 97, 88, 93, 91, 94, 80, 81, 86, 95, 91, 88, 96, 75, 90, 85, 89, 95, 85, 85, 86, 91.

A) Make a relative frequency histogram of the data using 7 classes.

B)According to Chebyshev, for the given data, between what two values could you expect to find 75% of the data?

if we get a “sign.” of 0.652, what is the chance of a Type I error if we reject the Null Hypothesis?

The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.

1. Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted. If required, round your answers to two decimal places.
   
   Q^* =
   
   Total Cost = $  
   
2. Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing cars. If required, round your answers to two decimal places.
   
   S^* =
   
   Total Cost = $  
   
3. What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year. If required, round your answer to two decimal places.
   
   Length of backorder period =  days
   
4. Would you recommend a no-backorder or a backorder inventory policy for this product? Explain. If required, round your answers to two decimal places.
   
   Recommendation would be backorder  inventory policy, since the maximum wait is only  days and the cost savings is $  .
   
5. If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies? If required, round your answers to two decimal places.
   
   Reorder point for no-backorder inventory policy is .
   
   Reorder point for backorder inventory policy is .

1. Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7,400 copies. The cost of one copy of the book is $12.5. The holding cost is based on an 14% annual rate, and production setup costs are $140 per setup. The equipment on which the book is produced has an annual production volume of 22,500 copies. Wilson has 250 working days per year, and the lead time for a production run is 16 days. Use the production lot size model to compute the following values:

   1. Minimum cost production lot size. Round your answer to the nearest whole number. Do not round intermediate values.
      
      Q^* =
      
   2. Number of production runs per year. Round your answer to two decimal places. Do not round intermediate values.
      
      Number of production runs per year =
      
   3. Cycle time. Round your answer to two decimal places. Do not round intermediate values.
      
      T =  days
      
   4. Length of a production run. Round your answer to two decimal places. Do not round intermediate values.
      
      Production run length =  days
      
   5. Maximum inventory. Round your answer to the nearest whole number. Do not round intermediate values.
      
      Maximum inventory =
      
   6. Total annual cost. Round your answer to the nearest dollar. Do not round intermediate values.
      
      Total annual cost = $  
      
   7. Reorder point. Round your answer to the nearest whole number. Do not round intermediate values.
      
      r =

As part of a study of wheat maturation, an agronomist selected a sample of wheat plants at random from a field plot. For each plant, the agronomist measured the moisture content from two locations: one from the central portion and one from the top portion of the wheat head. The agronomist hypothesizes that the central portion of the wheat head has more moisture than the top portion. What can the agronomist conclude with α = 0.01? The moisture content data are below.

Condition 1:

top portion

moisture content

wheat head

central portion
Condition 2:
wheat maturation

top portion

wheat head

central portion

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
test statistic =


d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

From the given information in each case below, state what you know about the P-value for a chi-square test and give the conclusion for a significance level of α = 0.01. Use Table 8 in Appendix A. (Enter your answers to three decimal places.)

(a) χ2 = 4.98, df = 2

< P-value <

(b) χ2 = 12.18, df = 6

< P-value <

(c) χ2 = 21.06, df = 9

< P-value <

(d) χ2 = 20.7, df = 4

P-value <

(e) χ2 = 5.86, df = 3

P-value >

7. An assembly line at a plant produces exactly 10000 widgets a day. Suppose that approximately 1 out of every 2000 fails a standards test and is thrown out. What is the probability that there will be 10 or more widgets thrown out on a given day?

8. There are 100 green balloons and 150 red balloons in a bag. Suppose we extract 10 balloons from the bag. (a) What is the exact probability that five of the balloons will be green? (b) Use Binomial Approximation to find the probability that exactly five of the balloons will be green. (c) Use Binomial Approximation to find the probability that no more than four of the balloons are green

A company needs to budget for fuel, they have to consider the weight of the shipment.

Average weight= 20,160 pounds

The CEO wonders if preferences have changed and you have to adjust the budget for fuel. Based on 14 shipments, the average weight has been 20,901 pounds with a sample standard deviation of 800 pounds. What should you conclude at the 99% confidence level?

Show your work on the calculated score (Commands from Excel)

Indicate what your calculated score is

Indicate and justify what your critical score is and determine if this sample average is statistically significant from the mean