Data in hrs/week:

1. Salient details of the analysis that was performed, including the estimate(s) obtained related to the question(s) considered, the associated test of the hypothesis (or hypotheses), and the related confidence interval(s) for the associated relevant parameters.

Explain Covariance and correlation.

Use duality to answer the following application.

Oz makes lion food out of giraffe and gazelle meat. Giraffe meat has 20 grams of protein and 40 grams of fat per pound, while gazelle meat has 40 grams of protein and 20 grams of fat per pound. A batch of lion food must contain at least 52,000 grams of protein and 78,000 grams of fat. Giraffe meat costs $1 per pound and gazelle meat costs $2 per pound. How many pounds of each should go into each batch of lion food in order to minimize costs? HINT [See Example 2.]

(giraffe meat, gazelle meat) = (_________) lb

What are the shadow costs of protein and fat?

protein $_______ per g

fat $________ per g

The Enormous State University Choral Society is planning its annual Song Festival, when it will serve three kinds of delicacies: granola treats, nutty granola treats, and nuttiest granola treats. The following table shows some of the ingredients required for a single serving of each delicacy, as well as the total amount of each ingredient available.

The society makes a profit of $6 on each serving of granola, $8 on each serving of nutty granola, and $3 on each serving of nuttiest granola. Assuming that the Choral Society can sell all that it makes, how many servings of each will maximize profits?

granola____________ serving(s)

nutty granola_________ serving(s)

nuttiest granola___________ serving(s)

How much of each ingredient will be left over?

toasted oats________ ounce(s)

almonds____________ ounce(s)

raisins__________ ounce(s)

A new nail salon business just opened, in their first week of business they decided that thy would conduct a promotion in which a customer's bill can be randomly selected to receive a discount. When a customer's bill is printed, a program in the cash register randomly determines whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0.2, that is, giving a discount to 20 percent of the bills in the long run. However, the owner is concerned that the program has a mistake that results in the program not generating the intended long-run proportion of 0.2.

(a) The owner selected a random sample of 100 bills and found that only 16 percent of them received discounts. The conditions for inference are met. Using the sample data collected by the owner, calculate a 95% confidence interval for the true proportion of bills that will receive a discount in the long run.

(b) Observing the value that you received in part a. Do you believe that the confidence interval provide convincing statistical evidence to indicate that the program is not working as intended?

An insurance agent randomly selected 10 of his clients and checked online price quotes for their policies. His summaries of the data are​ shown, where Diff is Local minus−Online.

Variable Count Mean StdDev

Local 10 884.200 316.487

Online 10 826.300 249.734

Diff 10 57.9000 181.582

Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to an online agent.

Use α= 0.05. HO​: μd=0 HA​: μd>0

Compute the test statistic and Find the​ P-value.

Could anyone please explain how to do this? I would appreciate it!

The judges of County X try thousands of cases per year. Although in a big majority of the cases disposed the verdict stands as rendered, some cases are appealed. Of those appealed, some are reversed. Because appeals are often made as a result of mistakes by the judges, you want to determine which judges are doing a good job and which ones are making too many mistakes.

The attached Excel file has the results of 182,908 disposed cases over a three year period by the 38 judges in various courts of County X. Two of the judges (Judge 3 and Judge 4) did not serve in the same court for the entire three-year period. Using your knowledge of probability and conditional probability you will make an analysis to decide a ranking of judges. You will also analyze the likelihood of appeal and reversal for cases handled by different courts.

Using Excel to calculate the following probabilities for each judge. Use the attached Excel file to fill in these numbers on the tables for each court. Each court is given on a separate tab.

The probability of a case being appealed for each judge.

The probability of a case being reversed for each judge.

The probability of a reversal given an appeal for each judge.

Probability of cases being appealed and reversed in the three courts.

Rank the judges within each court.

Only 1 dataset is post due to length of the question.

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

(a) Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.) The correlation of Wattage and Area is?

(b) Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.02 significance level. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

(c) Develop the regression equation for effective heating based on wattage. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) The regression equation is?

(d) Which heater looks like the “best buy” based on the size of the residual? (Round residual value to 2 decimal places.) The ______heater is the "best buy." It heats an area that is________ square feet larger than estimated by the regression equation.

Question 1 In the Payne County medical center, a surgical director selected a random sample of 37 nurses and found that the mean of their ages was 39.40. The sample standard deviation for the ages is 6.42. The director also selected a random sample of 32 physical therapists and found the mean of their ages was 36.77.

The sample standard deviation of ages for the physical therapists is 4.48.

A. [3] Give one reason why this data should not be analyzed as matched pairs.

B. [7] Find the 99% confidence interval of the differences in the average ages.
Group 1 is the nurses; group 2 is the physical therapists.
Assume that variances are unpooled; Satterthwaite’s formula gives DF = 64.285.

C. [3] Based on your interval, would you support or reject a hypothesis that nurses and physical therapists have the same average age? Briefly explain your reasoning. [If you didn’t find a confidence interval, use an interval from –1.11 to +6.08.]

Question 2

At the hospital, a study was done to see if there is a difference between the number of sick days taken by nurses and by physical therapists. Since nurses deal with sicker patients, the hospital director wants to see if nurses take significantly more sick days on average, compared to physical therapists.

For the 30 nurses with at least one year of experience, the mean of the number of sick days taken was 6.47 days with sample standard deviation s1 = 1.96. For the 22 physical therapists with data, the mean was 4.76 with sample standard deviation s2 = 1.53. At the α = 0.05 level, do nurses (group 1) take significantly more sick days?

A. [3 points] What are the null and alternative hypotheses? H0: H1:
B. [3] What is the rejection region for this test?

C. [5] Compute the test value. Hospital statisticians decide to pool variance for sick days.

D. [3] Make a decision and briefly explain why you made that decision. [If you didn’t get a test value, use 3.31.]

Zagat’s publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service.

a. Construct a scatter plot.

b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.

c. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem.

d. Predict the mean cost per person for a restaurant with a summated rating of 50.

e. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal?

We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data438.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.
(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?
Wages =   + LOS
t =     
P =  

(c) State carefully what the slope tells you about the relationship between wages and length of service.

This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope.
( , )

worker  wages   los     size
1       48.8329 97      Large
2       78.2535 28      Small
3       48.5138 22      Small
4       41.3975 34      Small
5       46.5544 22      Large
6       50.0827 36      Small
7       49.9522 30      Large
8       41.034  38      Large
9       42.8532 50      Large
10      42.9051 160     Small
11      60.7879 67      Large
12      63.7248 90      Small
13      44.9267 75      Small
14      66.4115 45      Large
15      54.5279 62      Large
16      38.777  33      Large
17      40.5469 74      Large
18      42.0242 33      Small
19      39.4129 151     Large
20      59.0103 145     Large
21      57.4567 17      Large
22      49.0608 38      Small
23      72.6341 141     Large
24      43.5226 36      Small
25      40.3436 56      Large
26      46.0549 88      Small
27      38.4406 133     Small
28      62.0137 44      Large
29      48.8695 116     Large
30      38.204  23      Large
31      44.858  83      Small
32      55.3133 21      Large
33      56.7109 16      Large
34      40.989  34      Small
35      50.3024 90      Large
36      39.6625 26      Large
37      38.9004 88      Large
38      54.0486 83      Small
39      39.6416 134     Large
40      54.4411 69      Small
41      43.3311 101     Small
42      52.6132 124     Small
43      51.0736 114     Large
44      40.7319 119     Small
45      86.2669 46      Large
46      44.7879 38      Small
47      61.0304 27      Large
48      37.5828 90      Large
49      79.3865 32      Small
50      60.6761 155     Large
51      56.5249 42      Large
52      45.8192 60      Large
53      42.2774 143     Large
54      37.538  38      Small
55      79.559  47      Small
56      46.9229 111     Large
57      66.448  55      Small
58      39.1776 96      Large
59      79.3531 119     Small
60      45.389  106     Large

I really don't understand how to do this problem. Can someone explain every step?

Minitab printout

One-Sample T: weight of cats

Descriptive Statistics (weight is in pounds)

N Mean StDev SE Mean 95% CI for μ
33 9.300 1.707 0.297 (8.694, 9.905) μ: mean of weight of cats Test Null hypothesis H₀: μ = 8.5
Alternative hypothesis H₁: μ ≠ 8.5
T-Value P-Value
2.69 0.011

a. Looking at the confidence interval estimate, write a confidence statement for the mean weight for all cats.
b. State your decision for the null hypothesis and show how you arrived at it.
c. Write your conclusion.
d. Can we safely say that the mean weight of all cats will be at least 8 pounds? Please give a reason for your answer.

A random sample of thirty-six 200-meter swims has a mean time of 3.009 minutes. The population standard deviation is 0.080 minutes. A 90​% confidence interval for the population mean time is (2.987,3.031).

Construct a 90​% confidence interval for the population mean time using a population standard deviation of 0.04 minutes. Which confidence interval is​ wider? Explain.

As a quality control​ manager, you are responsible for checking the quality level of AC adapters for tablet PCs that your company manufactures. You must reject a shipment if you find 5 defective units. Suppose a shipment of 46 AC adapters has 12 defective units and 34 non defective units. Complete parts​ (a) through​ (d) below assuming you sample 15 AC adapters. a) What is the probability that there will be no defective units in the​ shipment? b) What is the probability that there will be at least 1 defective unit in the​ shipment? c) What is the probability that there will be 5 defective units in the​ shipment? d) What is the probability that the shipment will be​ accepted?

6. The Humber Student Federation conducted a survey to determine the mean study time/week of students at the Lakeshore Campus. A sample of 18 students had a mean of 7.5 hours and a standard deviation of 2.2 hours. Assuming that the sampling distribution is about normal, calculate a 99% confidence interval for the mean study time all students at the Lakeshore Campus.