A credit score is used by credit agencies​ (such as mortgage companies and​ banks) to assess the creditworthiness of individuals. Values range from 300 to​ 850, with a credit score over 700 considered to be a quality credit risk. According to a​ survey, the mean credit score is 705.9. A credit analyst wondered whether​ high-income individuals​ (incomes in excess of​ $100,000 per​ year) had higher credit scores. He obtained a random sample of 39 ​high-income individuals and found the sample mean credit score to be 718.1 with a standard deviation of 81.7. Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the alphaequals0.05 level of significance. State the null and alternative hypotheses. Upper H 0​: mu ▼ less than not equals equals greater than nothing Upper H 1​: mu ▼ not equals less than greater than equals nothing ​(Type integers or decimals. Do not​ round.) Identify the​ t-statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Make a conclusion regarding the hypothesis. ▼ Reject Fail to reject the null hypothesis. There ▼ is is not sufficient evidence to claim that the mean credit score of​ high-income individuals is ▼ less than equal to greater than nothing.

The probability of winning the Powerball jackpot on a single given play is 1/175,223,510. Suppose the powerball jackpot becomes large, and many people play during one particular week. In fact, 180 million tickets are sold that week. Assuming all the tickets are independent of one another, then the number of tickets should be binomially distributed. The values of the parameters n and p in this binomial distribution are:

n=

p=

Then, use the binomial distribution to find the probability that there is one or more winning tickets sold.

______

If X = the number of winning tickets sold, find the mean and standard deviation of the random variable X.

Mean of X =  

Standard deviation of X =  

On the other hand, since the "times" between winning tickets should be independent of one another, the number of winning tickets per week could reasonably be modeled by a Poisson distribution.

The value of the parameter lambda in this Poisson distribution would be _____

The standard deviation of the number of tickets sold in a week (using the Poisson model) is _________

What does the Poisson model predict is the probability of having one or more winning tickets sold? _____

Then, use the binomial distribution to find the probability that there is one or more winning tickets sold. _________

a nursing student conducted a project at a physician's office. she took a medical history while the patient waited in the waiting room. she then reviewed the patient's medical record and retrieved the patient's medical record from the hospital used by the patient. she classified the patients into one of four groups.

1. the patients information matched the medical record

2. information that the patient had but the medical record did not contain

3. information in the medical record that the patient did not recall

4. information that was neither in the patient's recollection nor in the medical record

draw a cross table for this inserting the numbers 1-4 in the cells

A survey was undertaken by Bruskin/Goldring Research for Quicken to determine how people plan to meet their financial goals in the next year. Respondents were allowed to select more than one way to meet their goals. Thirty-one percent said that they were using a financial planner to help them meet their goals. Twenty-four percent were using family/friends to help them meet their financial goals followed by broker/accountant (19%), computer software (17%), and books (14%). Suppose another researcher takes a similar survey of 550 people to test these results.

a)  If 183 people respond that they are going to use a financial planner to help them meet their goals, is this proportion enough evidence to reject the 31% figure generated in the Bruskin/Goldring survey using α = 0.10.

The value of the test statistic is ________ & reject the null hypothesis/ fait to reject the null hypothesis

There is/ is not enough evidence to declare that the proportion is any different/ not any different than 0.31

b)  If 143 respond that they are going to use family/friends to help them meet their financial goals, is this result enough evidence to declare that the proportion is significantly lower than Bruskin/Goldring’s figure of 0.24 if α = 0.05?

The value of the test statistic is ________ & reject the null hypothesis/ fait to reject the null hypothesis

There is/ is not enough evidence to declare that the proportion is any different/ not any different than 0.24

It has long been stated that the mean temperature of humans is 98.6 degrees F. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F. They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3​ days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.3 degrees F and a sample standard deviation of 1 degrees F. Use the​ P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6 degrees F at the alpha equals 0.01 level of significance. State the hypotheses.

Upper H 0​: ▼ mu p sigma ▼ not equals less than equals greater than 98.6 degrees F

Upper H 1​: ▼ sigma mu p ▼ not equals equals less than greater than 98.6 degrees F

Find the test statistic. t 0 equals nothing ​(Round to two decimal places as​ needed.) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) What can be​ concluded?

A. Do not reject Upper H 0 since the​ P-value is not less than the significance level.

B. Do not reject Upper H 0 since the​ P-value is less than the significance level.

C. Reject Upper H 0 since the​ P-value is not less than the significance level.

D. Reject Upper H 0 since the​ P-value is less than the significance level.

In a study of the accuracy of fast food drive-through orders, Restaurant A had 266 accurate orders and 63 that were not accurate.

a. Construct a 90% confidences interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: .0179<p<.0.249. What do you conclude?

The authors of the article “Accommodating Persons with AIDS: Acceptance and Rejection in Rental Situations” (Journal of Applied Social Psychology [1999]: 261-270) stated that, even though landlords participating in a telephone survey indicated that they would generally be willing to rent to persons with AIDS, they wondered whether this was true in practice. To investigate, the researches independently selected two random samples of 80 advertisements for rooms for rent from newspapers advertisements in three large cities. An adult male caller responded to each ad in the first sample of 80 and inquired about the availability of the room and was told that the room was still available in 61 of these calls. The same caller also responded to each ad in the second sample. In these calls, the caller indicated that he was currently receiving some treatment for AIDS and was about to be released from the hospital and would require a place to live. The caller was told that a room was available in 32 of these calls. Based on this information, the authors concluded that “reference to AIDS substantially decreased the likelihood of a room being described as available”. Do the data support this conclusion? (Use ? = 0.01)

role playing games like dungeons & dragons use many different types of dice. suppose that a SIX sided die has faces marked 1,2,3,4,5,6. The intelligence of a character is determined by rolling this die twice and adding 1 to the sum of the spots. The faces are equally likely and the two rolls are independent. what is the average (mean) intelligence for such characters?

how spread out are their intelligence , as measured by the standard deviation of the distribution?(round your answer to four decimal places)

The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three others were sprayed with Action. When the grapes ripened, 400 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 380 vines sprayed with Action were checked. The results are:

At the 0.10 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Hint: For the calculations, assume the Pernod 5 as the first sample.

1. State the decision rule. (Negative amounts should be indicated by a minus sign. Do not round the intermediate values. Round your answers to 2 decimal places.)

2. Compute the pooled proportion. (Do not round the intermediate values. Round your answer to 2 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Do not round the intermediate values. Round your answer to 2 decimal places.)

4. What is your decision regarding the null hypothesis?

• Reject

• Fail to reject

Probability Mass Functions, Random Variables

Find a table of the Binomial random variable (include a picture of the table in your submission) and obtain the probability that in 20 independent trials, each of which has probability of success equal to 0.1, the number of successes is less than or equal to 3.

Repeat the problem using instead of a Binomial a Poisson with suitable parameter lambda.

A university offers finance courses numbered 1,2,3,4,5 and accounting courses numbered 1,2,3,4,5,6. Let F be the event of selecting a finance course, A the event of selecting an accounting course, E the event of selecting an even numbered course, and O the event of selecting an odd course. Selecting the accounting course number 3 is an example of which of the following events? Select all correct answers. Select all that apply: A AND O F OR E F AND O F OR O E′ A′

4. (a) Describe the advantages and disadvantages of using a stratified sample design in a survey. Also, what information would you need to create the strata.

(b) Describe the advantages and disadvantages of using a cluster sample design in a survey.

(c) There are various ways of doing cluster sampling. For example, there are one-or two-stage sampling and clusters can be selected with equal or unequal (pps) selection probabilities. The choice of which design is better depends on the relative sources of variation and the relative costs of sampling within and between clusters. i. What would the population have to be like for a two-stage cluster sample design to give better results than a one-stage cluster sample? ii. Describe an example where unequal selection of clusters would give more precise estimates than an equal selection of clusters.

(d) What is the design effect and in general terms (that is, an exact formula is not required) how is it calculated?

(e) For stratified and cluster designs would you expect the design effect to be greater, less than or approximately equal to zero? Clearly explain why you expect this.

Perriot's Restaurant purchased kitchen equipment on January 1, 2014. The value of the kitchen equipment decreases by 15% every year. On January 1, 2016, the value was $14,450.

a) Find an exponential model for the value, V, of the equipment, in dollars, t years after January 1, 2016.

b) What is the rate of change in the value of the equipment on January 1, 2016?

c) What was the original value of the equipment on January 1, 2014?

d) How many years after January 1, 2014 will the value of the equipment have decreased by half?

1 1. Use "DOW_Characteristics" data in Chapter1.xlsx to answer the following questions. For questions that require Excel, include the appropriate output (copy + paste) along with an explanation. Data description: The accompanying table shows a portion of the 30 companies that comprise the Dow Jones Industrial Average (DJIA). The second column shows the year that the company joined the DJIA (Year). The third column shows each company’s Morningstar rating (Rating). (Five stars is the best rating that a company can receive, indicating that the company’s stock price is undervalued and thus a very good buy. One star is the worst rating a company can be given, implying that the stock price is overvalued and a bad buy.) Finally, the fourth column shows each company’s stock price as of March 17, 2017 (Price in $).

Questions: a. Are data in the table from a sample or from a population? Explain.

b. Are data in the table time series data or not? Explain

c. What is the measurement scale of the Year data? What are the strengths of this type of data? What are the weaknesses?

d. What is the measurement scale of Morningstar’s star-based rating system? Summarize Morningstar’s star-based rating system for the companies in tabular form. Let 5 denote *****, 4 denote ****, and so on. What information can be extracted from these data?

e. What is the measurement scale of the Stock Price data? What are its strengths?

f. List the qualitative and quantitative variables in the data table.

1. Chain Rule and the Markov Rule

1. You as a sports analyst are modeling the free throw success of Lebron James. You are asked to predict the probability that Lebron will make four free throws in serial succession during an important game that takes place in the opposite team’s venue.

Based on your data of Lebron’s previous free throws, you estimate that the median probability (0.5 below and 0.5 above) of a single free throw by Lebron under a wide range of expected conditions is 0.75. Also, estimate that the probability of free throw 2 given he made free throw 1 is P(2|1) = 0.8. Also you estimate that the Pr of free throw 3 given he made free throw 2 with kudos is P(3|2) = 0.9. But because of the extreme conditions at the important game in the opposite team’s site, you estimate that the Pr he makes free throw 4 given he made free throw 3 is 0.7.

Using these data, write the expression for and predict to 2 sd the Pr of success of four free throws in succession. Assume that the Pr he makes the first free throw is his median value of 0.75. As in b) assume the Markov Rule in which the primary dependency is with the previous free throw and further back free throws are less influential and considered independent for this analysis. Also, calculate the mean value and variance, and standard deviation of the probabilities where each probability value is equally weighted. Finally write an expression and calculate the numerical value of P(1,2,3,4) to two standard deviations, which represents uncertainty management of estimating the epistemic uncertainty of the probability values.

               Mean Probabilities=

Variance =

                Standard Deviation =  

P(1,2,3,4) =      to two standard deviations, which represents uncertainty management of epistemic uncertainty in the estimated probability values.

1. b. Now predict the probability to 2 sd of Lebron’s making 4 free throws in series if each free throw is considered independent of all of the other free throw attempts. Use Lebron’s median Pr value of success = 0.75.

P(1,2,3,4) =

Assume the same standard deviation calculated in a:

P(1,2,3,4) =        to two standard deviations exhibiting an estimate of epistemic uncertainty in the analysis. Do the results for c) and d) agree within the combined estimated uncertainties in the two values?

.