An insurance company issues a one-year $1,000 policy insuring against an occurrence A that historically happens to 3 out of every 100 owners of the policy. Administrative fees are $25 per policy and are not part of the company's "profit." How much should the company charge for the policy if it requires that the expected profit per policy be $60? [HINT: If C is the premium for the policy, the company's "profit" is C − 25 if A does not occur, and C − 25 − 1,000 if A does occur.]

=$?

3.2

Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Let x be a random variable representing time to failure (in hours) at 90% breaking strength.

(a) Find the range.


(b) Use a calculator to calculate Σx and Σx². (Round your answers to two decimal places.)

(c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (Round your answers to two decimal places.)

(d) Use the results of part (c) to compute the coefficient of variation. (Round your answer to the nearest whole number.)
%

What does this number say about time to failure?

The standard deviation of the time to failure is just slightly smaller than the average time.The coefficient of variation says nothing about time to failure.    The standard deviation of the time to failure is just slightly larger than the average time.The standard deviation is equal to the average.

Why does a small CV indicate more consistent data, whereas a larger CV indicates less consistent data? Explain.

A small CV indicates more consistent data because the value of s in the numerator is smaller.A small CV indicates more consistent data because the value of s in the numerator is larger.    

Consider sample data with

x = 8

and

s = 2.

(a) Compute the coefficient of variation.


(b) Compute a 75% Chebyshev interval around the sample mean.

1. Acompanysellinglicensesofnewe-commercesoftwareadvertisedthatfirmsusingthissoftware could obtain, on average during the first year, a minimum yield (in cost savings) of 20 percent on average on their software investment. To disprove the claim, we checked with 10 different firms which used the software. These firms reported the following cost-saving yields (in percent) during the first year of their operations:

   {17.0, 19.2, 21.5, 18.6, 22.1, 14.9, 18.4, 20.1, 19.4, 18.9}.

   1. Do we have significant evidence to show that the software company’s claim of a minimum of 20 percent in cost savings was not valid? Test using α = 0.05.

   2. Compute a 95% confidence interval for the average cost-saving yield estimate.

You are Susan Dean, a 35 year old woman who has always been interested in owning your own business. You graduated from Gorham HS, attended SMCC, eventually transferring to USM where you earned a bachelor’s degree in Business with a major in Marketing. Eventually you went to graduate school and earned a Master’s of Business Administration (MBA). For the last 10 years you have worked as a marketing specialist/management specialist with Yum! Brands, Inc. where you helped management open several Taco Bells and Pizza Huts in southern Maine. In addition, you evaluated several underperforming stores that had to be closed. After contacting several major corporations you find that McDonalds is the only major brand looking to open another store in the town of Gorham near the USM campus. There is a Burger King in the area. You in fact actually worked at McDonalds when you were a youngster. You have decided that you would like to open a McDonald’s franchise in this area near USM. Your grandparents have left you with a significant amount of money for which you are grateful. You would like to use this towards your new business adventure. But you will need to finance the remaining balance. You apply for a business loan to a local bank. The bank requires you to submit a detailed business plan. This business plan will include projections for operating costs, revenue stream, profits, human resource needs, your business strategy, etc. There are multiple topics that have to be analyzed and for which projections have to be made. Because of this you will have to conduct a survey(s) in the Gorham region to assess multiple demographic, supply/demand issues, and other topics.

Discussion Question/Directions:

You are Susan Dean. You need to discuss issues for which you think a statistical study would be helpful (in obtaining the information needed for your business plan). his could be demographic information, assessing the desire for a McDonald’s in the region, traffic studies, household make up, what the projected demand would be, etc. There are hundreds of topics to zero in on. What topics do you think are important to know before you invest your money into such an important undertaking? What type of statistical study should be done? What types of data will you need to collect? How will you collect your data? How much do you think it will cost to gather your information?

I am trying to find an appropriate statistical test to run for a research study using someone else's gathered data (so that no IRB process is needed). In their data they present:

Likelihood of Falling Asleep:

Never 17

Seldom 22

Moderate 15

High 12

Use of napping during duty:

Never 27

Rarely 19

Sometimes 16

Often 4

Both of these seem to be independent variables, but is there a way to show a relationship (or lack thereof) without a dependent variable. In this case the dependent variable could be "pilot" of which 66 were surveyed for the study that I am taking the data from. Trying accurately to show whether or not the likelihood of falling asleep in the cockpit is related to whether or not the pilot naps on duty outside of the cockpit.

Thanks!

Two equal groups of seedlings, and equal in height, were selected for an experiment. One group of seedlings was fed Fertilizer A, and the other group with Fertilizer B. The mean heights of the two groups of seedlings, their standard deviations, and sample sizes are listed below. Assume simple random sampling, independence, and normally distributed data. Alpha = 0.025. Sample Mean Height (inches, Std Deviation (inches), Sample Size Fertilizer A 12.92, 0.25, 15 Fertilizer B 12.63, 0.20, 13 What is the null hypothesis?

Using the data in the previous question, what is the critical t value using the simplified textbook method and Tables when testing the claim that Fertilizer A is significantly greater than Fertilizer B?   Record the answer to three decimal places (x.xxx).

Using the data from the previous question, what is the t-statistic rounded off to one decimal place ? (x.x)

Question 1 - Binomials

Eighty percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the probability that among the next 15 applicants:

1. Exactly 6 will be accepted?
2. At least 10 will be accepted?
3. Exactly 3 will be rejected?
4. Eight or more will be accepted?
5. Determine the expected number of accepted students. Remember you are talking about people. Work is required.
6. Compute the standard deviation.- Make sure you have looked at page 245. Work is required.

The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.

1. Does a linear trend appear to be present?
   
2. use simple linear regression to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)
   
   y-intercept, b₀ =
   
   Slope, b₁ =
   
   MSE =
3. Use the trend equation from part (b) to forecast the percentage of adults next year (year 16 of the study) who will report that they exercise for 30 or more minutes at least three times per week. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)
   
   %
4. Use the trend equation from part (b) to forecast the percentage of adults three years from now (year 18 of the study) who will report that they exercise for 30 or more minutes at least three times per week. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

A procurement specialist has purchased 25 resistors from Vendor 1 and 35 resistors from Vendor 2. Each resistor’s resistance was measured and reported in Problem 4 spreadsheet of Homework 2.xlsx. You want to compare mean performance. Use R, and draw conclusions with 0.05 significance. a. First perform the appropriate test to determine whether to assume equal or unequal dispersions of resistance for the two vendors. b. Based on your answer in part a, compare mean performance of the vendors with the appropriate ? test.

Current technology uses lasers for the inspection of solder-joint defects on printed circuit boards (PCBs). A particular manufacturer of laser-based inspection equipment claims that its product can inspect on average at least 10 solder joints per second when the joints are spaced 0.1 inch apart. The equipment was tested by a potential buyer on 30 different PCBs. In each case, the equipment was operated for exactly one second. The number of solder joints inspected on each run is found in the Homework 2.xlsx file. The potential buyer wants to know whether the sample data refute the manufacturer’s claim. Formulate appropriate hypotheses and answer with 95% confidence.

GMAT (assume to be distributed Normally with a mean 500 and a standard deviation of 100) and GRE (assume to be distributed Normally with a mean 300 and a standard deviation of 15) to select potential candidates. Candidate A has a GMAT score of 650 while candidate B has a GRE score of 320. Who is a better candidate and why?

(Problems 1.19, 1.23 and 2.4. from KNN) The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student’s grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X).

3.897 21
3.885 14
3.778 28
2.540 22
3.028 21
3.865 31
2.962 32
3.961 27
0.500 29
3.178 26
3.310 24
3.538 30
3.083 24
3.013 24
3.245 33
2.963 27
3.522 25
3.013 31
2.947 25
2.118 20
2.563 24
3.357 21
3.731 28
3.925 27
3.556 28
3.101 26
2.420 28
2.579 22
3.871 26
3.060 21
3.927 25
2.375 16
2.929 28
3.375 26
2.857 22
3.072 24
3.381 21
3.290 30
3.549 27
3.646 26
2.978 26
2.654 30
2.540 24
2.250 26
2.069 29
2.617 24
2.183 31
2.000 15
2.952 19
3.806 18
2.871 27
3.352 16
3.305 27
2.952 26
3.547 24
3.691 30
3.160 21
2.194 20
3.323 30
3.936 29
2.922 25
2.716 23
3.370 25
3.606 23
2.642 30
2.452 21
2.655 24
3.714 32
1.806 18
3.516 23
3.039 20
2.966 23
2.482 18
2.700 18
3.920 29
2.834 20
3.222 23
3.084 26
4.000 28
3.511 34
3.323 20
3.072 20
2.079 26
3.875 32
3.208 25
2.920 27
3.345 27
3.956 29
3.808 19
2.506 21
3.886 24
2.183 27
3.429 25
3.024 18
3.750 29
3.833 24
3.113 27
2.875 21
2.747 19
2.311 18
1.841 25
1.583 18
2.879 20
3.591 32
2.914 24
3.716 35
2.800 25
3.621 28
3.792 28
2.867 25
3.419 22
3.600 30
2.394 20
2.286 20
1.486 31
3.885 20
3.800 29
3.914 28
1.860 16
2.948 28

1.Obtain the least squares estimates of β₀ and β₁ , and state the estimated regression function. You may use the R commands:  

> gpa.model<-lm(GPA~ACT,data=gpa)

> summary(gpa.model)

Estimate for β₀=____ (round answer to 5 decimal places. If the answer is 0.12345, please DO enter the zero before the decimal point)

Estimate for β₁=____(round answer to 5 decimal places. If the answer is 0.12345, please DO enter the zero before the decimal point)

2.

1. b. Plot the estimated regression function and the data. Does the estimated regression function appear to fit the data well?

   > plot(GPA~ACT,data=gpa)

   > abline(gpa.model)

   Yes

     No

3. Obtain a point estimate of the mean freshman GPA for students with ACT test score X=30. Round answer to 5 decimal places.

4.obtain the residuals ei.

>gpa.model$residuals

Enter here the residual corresponding to the 15th observation=____ (round answer to 5 decimal places. )

Do they sum to zero? use the function sum(), see if you get something close to zero.

Answer: ____(Yes/No)

5.Estimate for σ² =____ Round answers to 5 decimal places. Enter 0 before decimal point.

Estimate for  σ = ____ Round answers to 4 decimal places. Enter 0 before decimal point.

Obtain a 99 percent confidence interval for β1. You can use the following command. You need to write the level as a number, not a percent.

>confint(gpa.model,level= )

Lower bound = ____, Upper bound = ____ Round answers to 5 decimal places. Write the 0 before the decimal point.

Does it include zero? ____(Yes/No)

7.

We would like to test whether or not a linear association exists between student’s ACT Score (X) and GPA at the end of the freshman year (Y). State the hypothesis of the test:

8.

Test, using a t-test, whether or not a linear association exists between student’s ACT Score (X) and GPA at the end of the freshman year (Y). Using a level of significance of .01, compute the following.

The test statistic is: T = ____ Round answer to 2 decimals.

The p-value is = ____ Round answer to 5 decimals.

9.After testing whether or not a linear association exists between student’s ACT Score (X) and GPA at the end of the freshman year (Y), write down the conclusion of the test.

A retail giant, Mississippi, sells books on its website. The book Lisa Panner and the Accountant’s Ledger (LP for short) is sold in the hardcover version, paperback version, audiobook version, or the e-book version to be read on its proprietary device Ignite. It is known that no one buys both hardcover and paperback of LP, and no one buys both hardcover and e-book. It is also known that no customer buys all three of paperback, e-book and audiobook. Of the customers interested in LP, Mississippi has found that 15% have bought the hardcover, 35% have bought the paperback, 30% have bought the audiobook and 25% have bought the e-book. Furthermore, 40% have bought either the hardcover or the audiobook, and 10% have bought both the paperback and the audiobook.

(a) What fraction of the interested customers have bought both the hardcover and the audiobook?

(b) What fraction of the interested customers have bought exactly one of the paperback or the audiobook?

(c) (Somewhat hard) If 5% of interested customers have bought both audiobook and e-book, what fraction have bought only the audiobook? (Hint: Drawing the Venn diagram will be helpful. Try to break the set of customers who bought an audiobook into mutually exclusive sets so that you can use additivity.)

apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).

#1. What information does a correlation coefficient convey?

#2. State whether each of the following is an example of a positive correlation or a negative correlation.

a. Higher education level is associated with a larger annual income

. b. Increased testosterone is associated with increased aggression.

c. The smaller the class size, the more students believe they are receiving a quality education.

d. Rising prices of apples are associated with the sale of fewer apples.

#3. Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?

a. A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation.

b. A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas. \

c. A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal.

A local bank has two branches, one in Standish and the other in Limerick. To determine whether the wait time at the drive-through was different for the branches, the director of the bank had the manager at each branch use security camera footage to randomly select 40 customers who used the drive-through and to determine the wait time. The average wait time for the sample for the Standish branch was 93.12 seconds with a standard deviation of 14.65 seconds. The average wait time for the sample for the Limerick branch was 107.36 seconds with a standard deviation of 16.14 seconds. Let μ1 be the population mean wait time for drive-through customers at the Standish branch, and let μ2 be the population mean wait time for drive-through customers at the Limerick branch. The alternative hypothesis for this test is Ha:μ1−μ2≠0. Assume that the population standard deviations of the wait time for the two branches are equal. If the p-value of the hypothesis test is less than 0.01 and the significance level is α=0.10, what conclusion could be made about the population mean wait times for customers at the two branches?

Select all that apply:

A) Reject the null hypothesis.

B) Fail to reject the null hypothesis.

C) The conclusion of the hypothesis test is that there is sufficient evidence to suggest that the population mean wait time for customers at the Standish branch is different than the population mean wait time for customers at the Limerick branch.

D) The conclusion of the hypothesis test is that there is insufficient evidence to suggest that the population mean wait time for customers at the Standish branch is different than the population mean wait time for customers at the Limerick branch.