A test for a disease gives a correct positive result with a probability of 0.95 when the disease is present but gives an incorrect positive result (false positive) with a probability of 0.15 when the disease is not present. If 5% of the population has the disease, and Jean tests positive to the test, what is the probability Jean really has the disease?

10. According to the National Health and Nutrition Examination Survey and the Epidemiologic Follow-up Study the mean systolic blood pressure for individuals aged 25 to 59 is 127.3 with a standard deviation of 20.2. A sample measurement of systolic blood pressure from 15 EDUR 8131 Statistics students is taken to learn whether EDUR 8131 students have blood pressure that differs from the national average.

(a) Perform a one sample Z test on these data to learn whether a difference in blood pressure exists:

• present calculated Z test value, and

• write a brief conclusion about your finding. Use α = .05 for hypothesis testing.

(b) Construct a 95% confidence interval about the sample mean for these data. Sample Systolic Blood Pressure: 143 176 131 95 139 145 169 139 181 161 151 195 132 175 143

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in a town in Colorado. The x distribution has a mean μ of approximately 75°F and standard deviation σ of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table.

(i) Remember that μ = 75 and σ = 8. Examine the figure above. Write a brief explanation for columns I, II, and III in the context of this problem.

This answer has not been graded yet.

(ii) Use a 1% level of significance to test the claim that the average daily July temperature follows a normal distribution with μ = 75 and σ = 8.(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are different.H₀: The distributions are different.
H₁: The distributions are the same.     H₀: The distributions are the same.
H₁: The distributions are the same.H₀: The distributions are the same.
H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo     

What sampling distribution will you use?

normalbinomial     Student's tchi-squareuniform

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100     0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, the evidence is sufficient to conclude that the average daily July temperature does not follow a normal distribution.At the 1% level of significance, the evidence is insufficient to conclude that the average daily July temperature does not follow a normal distribution.    

Using samples of 194 credit card statements, an auditor found the following:
Use Table-A.

a. Determine the fraction defective in each sample. (Round your answers to 4 decimal places.)
  

b.If the true fraction defective for this process is unknown, what is your estimate of it? (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Estimate              %

c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? (Round your intermediate calculations and final answers to 4 decimal places.)
  

d.What control limits would give an alpha risk of .03 for this process? (Round your intermediate calculations to 4 decimal places.Round your "z" value to 2 decimal places and other answers to 4 decimal places.)
  

z =  ,     to  

e.What alpha risk would control limits of .0470 and .0098 provide? (Round your intermediate calculations to 4 decimal places.Round your "z" value to 2 decimal places and "alpha risk" value to 4 decimal places.)
  

z =  , alpha risk =  

f.Using control limits of .0470 and .0098, is the process in control?

• no

• yes

g.Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? (Round your intermediate calculations and final answers to 2 decimal places.)

h.Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control?

• Yes

• No

Describe an application of multiple discriminant analysis that is specific to your industry(Scientific Research) or to your academic interests. Explain why this technique is suitable in terms of measurement scale of variables and their roles.

A small car dealer, who is eager to estimate his inventory cost, can hold up
to 4 cars in the showroom. The periodic demand for the cars is following a Poisson
distribution with mean 2, except for the maximum inventory level. In the case of
maximum inventory level, the dealer makes a special discount by offering a price much
below the market which results in depletion of its entire inventory. Once all the cars are
sold, the dealer immediately orders 3 or 4 cars with equally likely probabilities. Apart
from maximum and minimum inventory levels, the dealer can sell all his cars and also
seek to refill its inventory. The Inventory cost is given as; $500 per car per period.
(a) Construct the transition probability matrix, by properly defining the states and the
state space.
(b) Find the average inventory holding cost per period.

Two marbles are drawn at random and with replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events: A = {two red marbles are drawn} B = {two green marbles are drawn} C = {two blue marbles are drawn} D = two marbles of the same color are drawn}

Find the probabilities of the following events:

(a) P(A), P(B), P(C), and P(D).

(b) P(A|D).

Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to nuts. Let n1,n2 be the sample size of a random sample for male and female, respectively. Assume two samples are indepedent. Let X1,X2 be the number of male and female who have allergy to nuts in the random sample, respectively.

(1) For parameters p1,p2, and p1−p2, find one unbiased estimator for each of them. And show why they are unbiased.

(2)Derive the formula for the standard error of those estimators in (1). Note that V(X−Y)=V(X)+V(Y) for two independent rv's X,Y.

(3)For given samples, let n1=100,n2=150,x1=5,x2=9. Compute the the value of those estimators in (1).

4) For given samples, let n1=100,n2=150,x1=5,x2=9. Compute the estimated standard errors of those estimators in (2)

Given a random variable XX following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5Y=0.4X+5 is also normal.

(1)(2pts) Find the distribution of YY, i.e. μY,σY.μY,σY.

(2)(3pts) Find the probabilities P(−4<X<0),P(−1<Y<0).P(−4<X<0),P(−1<Y<0).

(3)(3pts) Find the probabilities P(−4<X¯<0),P(3<Y¯<4).P(−4<X¯<0),P(3<Y¯<4).

(4)(4pts) Find the 53th percentile of the distribution of X.

When people buy a certain type of laptop, there are three most popular upgrading options: upgrade the RAM (A), upgrade the hard drive (B), upgrade the graphic card (C). If 50% of all purchasers request A, 40% request B, 36% request C, 66% request A or B, 76% request A or C, 66% request B or C, and 86% request A or B or C, determine the probabilities of the following events.

(1) One randomly selected purchaser will request at least one of the three options.

(2) One randomly selected purchaser will select none of the three options.

(3) One randomly selected purchaser will request only option C and not neither of the other two options.

(4) One randomly selected purchaser will request exactly one of the three options.

Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal.

(1)Find the distribution of Y, i.e. μy,σy

(2)Find the probabilities P(−4<X<0),P(−1<Y<0)

(3)Find the probabilities P(−4<X¯<0),P(3<Y¯<4)

(4)Find the 53th percentile of the distribution of X

Healthy Lifestyles

The Centers for Disease Control and Prevention (CDC) in Atlanta, Georgia, is the government agency responsible for disease-related issues in the United States. The CDC coordinates efforts to counteract outbreaks of diseases and funds a variety of medical and health research studies. The CDC also serves as a central clearinghouse for health-related data.

The CDC conducts the annual Behavioral Risk Factor Surveillance Survey. The survey measures a whole series of lifestyle characteristics that relate to health and longevity, such as smoking and use of seat belts. The survey compiles data on a stateby-state basis. Not all states are surveyed.

The data set from the 1990 Behavioral Risk Factor Surveillance Survey is on the accompanying CD in the file named HEALTHY. All numbers are percentages, and asterisks indicate the missing data for that state.

Your task is to prepare a summary of these data. Your report is to be issued to major news organizations, such as the Associated Press, and will appear in major newspapers around the United States. For this reason, it would be inappropriate to use technical jargon in your report.

Your boss has suggested a few general ideas about what is likely to appeal to your target audience. As you study the data, you might find other things worth including.

Questions

1. Report any interesting (i.e., unexpected, humorous, or odd) differences between states.

2. Devise a weighted index of all seven lifestyle variables. The weighted index is to serve as an overall or composite measure of healthy lifestyles. Apply your weight to the states of Minnesota, Florida, and California as an example of what your weighted index shows.

3. Discuss any noteworthy limitations of the survey or data set.

A study of 420,047 cell phone users found that 130 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0223​% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell​ phones? Why or why​ not?

A. No, because 0.0223​% is not included in the confidence interval.

B.No​, because 0.0223% is included in the confidence interval.

C. Yes, because 0.0223% is included in the confidence interval.

D. Yes, because 0.0223​% is not is not included in the confidence interval.

A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 95​% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi? 0.52  0.68  0.10  0.95  1.27  0.50  0.89

What is the confidence interval estimate of the population mean muμ​?

nothing ppmless than<muμless than<nothing ppm ​(Round to three decimal places as​ needed.)

Does it appear that there is too much mercury in tuna​ sushi?

A.​Yes, because it is possible that the mean is greater than 1 ppm.​ Also, at least one of the sample values exceeds 1​ ppm, so at least some of the fish have too much mercury.

B. ​No, because it is not possible that the mean is greater than 1 ppm.​ Also, at least one of the sample values is less than 1​ ppm, so at least some of the fish are safe.

C. ​No, because it is possible that the mean is not greater than 1 ppm.​ Also, at least one of the sample values is less than 1​ ppm, so at least some of the fish are safe.

Twelve different video games showing substance use were observed and the duration of times of game play​ (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct an 80​% confidence interval estimate of sigma​, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution. 4251 4261 4551 4691 4423 4 728 4797 4473 4421 4496 3949 4524

The confidence interval estimate is blank sec < <blank sec.