. Refer to the accompanying table showing results from a Chembio test for Hepatitis C among HIV-infected patients.

a. Find the probability of selecting a subject with a positive test result, given that the subject does not have hepatitis C. Why is this case problematic for test subjects?

b. Find the probability of selecting a subject with a negative test result, given that the subject has hepatitis C. What would be an unfavorable consequence of this error?

c. Find the positive predictive value for the test. That is, find the probability that a subject has hepatitis C, given that the test yields a positive result. Does the result make the test appear to be effective?

d. Find the negative predictive value for the test. That is, find the probability that a subject does not have hepatitis C, given that the test yields a negative result. Does the result make the test appear to be effective?

Typing errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell‑checking software will catch nonword errors but not word errors. Human proofreaders catch 70%70% of word errors.

You ask a fellow student to proofread an essay in which you have deliberately made 1010 word errors.

(a) If ?X is the number of word errors missed, what is the distribution of ?X ? Select an answer choice.

?X is approximately Normal with ?=3μ=3 and ?=1.45σ=1.45

?X is binomial with ?=10n=10 and ?=0.3p=0.3

?X is binomial with ?=10n=10 and ?=0.7p=0.7

?X is Normal with ?=7μ=7 and ?=1.45σ=1.45

If ?Y is the number of word errors caught, what is the distribution of ?Y ? Select an answer choice.

?Y is binomial with ?=10n=10 and ?=0.7p=0.7

?Y is binomial with ?=10n=10 and ?=0.3p=0.3

?Y is approximately Normal with ?=3μ=3 and ?=1.45σ=1.45

?Y is Normal with ?=7μ=7 and ?=1.45σ=1.45

(b) What is the mean number of errors caught? (Enter your answer as a whole number.)

mean of errors caught =

What is the mean number of errors missed? (Enter your answer as a whole number.)

mean of errors missed =

(c) What is the standard deviation of the number of errors caught? (Enter your answer rounded to four decimal places.)

standard deviation of the number of errors caught =

What is the standard deviation of the number of errors missed? (Enter your answer rounded to four decimal places.)

standard deviation of the number of errors missed =

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 70 cookies. The mean is 22.24 and the standard deviation is 2.44. .Construct a 98​% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies. How do I find the degree of freedom, which is 69, using the chi critical value table? 69 is not listed on there, just 60 and 70. Not sure how to use my TI-84 calculator to figure it out.

An article in Computers & Electrical Engineering, “Parallel simulation of cellular neural networks” (1996, Vol. 22, pp. 61–84) considered the speed-up of cellular neural networks (CNN) for a parallel general-purpose computing architecture based on six transputers in different areas. The data follow: 3.775302 3.350679 4.217981 4.030324 4.639692 4.139665 4.395575 4.824257 4.268119 4.584193 4.930027 4.315973 4.600101 Round your answers to 3 decimal places. Assume population is approximately normally distributed. (b) Construct a 99% two-sided confidence interval on the mean speed-up. Enter your answer; confidence interval, lower bound ≤μ≤ Enter your answer; confidence interval, upper bound (c) Construct a 99% lower confidence bound on the mean speed-up. Enter your answer in accordance to the item c) of the question statement ≤μ

All Greens is a franchise store that sells house plants and lawn and garden supplies. Although All Greens is a franchise, each store is owned and managed by private individuals. Some friends have asked you to go into business with them to open a new All Greens store in the suburbs of San Diego. The national franchise headquarters sent you the following information at your request. These data are about 27 All Greens stores in California. Each of the 27 stores has been doing very well, and you would like to use the information to help set up your own new store. The variables for which we have data are detailed below. x1 = annual net sales, in thousands of dollars x2 = number of square feet of floor display in store, in thousands of square feet x3 = value of store inventory, in thousands of dollars x4 = amount spent on local advertising, in thousands of dollars x5 = size of sales district, in thousands of families x6 = number of competing or similar stores in sales district A sales district was defined to be the region within a 5 mile radius of an All Greens store. I really need help with the bolded areas. Thank you.

x1 x2 x3 x4 x5 x6 231 3 294 8.2 8.2 11 156 2.2 232 6.9 4.1 12 10 0.5 149 3 4.3 15 519 5.5 600 12 16.1 1 437 4.4 567 10.6 14.1 5 487 4.8 571 11.8 12.7 4 299 3.1 512 8.1 10.1 10 195 2.5 347 7.7 8.4 12 20 1.2 212 3.3 2.1 15 68 0.6 102 4.9 4.7 8 570 5.4 788 17.4 12.3 1 428 4.2 577 10.5 14.0 7 464 4.7 535 11.3 15.0 3 15 0.6 163 2.5 2.5 14 65 1.2 168 4.7 3.3 11 98 1.6 151 4.6 2.7 10 398 4.3 342 5.5 16.0 4 161 2.6 196 7.2 6.3 13 397 3.8 453 10.4 13.9 7 497 5.3 518 11.5 16.3 1 528 5.6 615 12.3 16.0 0 99 0.8 278 2.8 6.5 14 0.5 1.1 142 3.1 1.6 12 347 3.6 461 9.6 11.3 6 341 3.5 382 9.8 11.5 5 507 5.1 590 12.0 15.7 0 400 8.6 517 7.0 12.0 8

(a) Generate summary statistics, including the mean and standard deviation of each variable. Compute the coefficient of variation for each variable. (Use 2 decimal places.) x s CV x1

(b) For each pair of variables, generate the correlation coefficient r. For all pairs involving x1, compute the corresponding coefficient of determination r2. (Use 3 decimal places.) r r2

x1, x2

(c) Perform a regression analysis with x1 as the response variable. Use x2, x3, x4, x5, and x6 as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x1 can be explained by the corresponding variations in x2, x3, x4, x5, and x6 taken together? (Use 1 decimal place.)

99.3%

(d) Write out the regression equation. (Use 2 decimal places for x3 and x6. Use 1 decimal place otherwise.)

x1=-18.86+16.2x2+.18x3+11.53x4+13.58x5+(-5.31x6)

If 12 new competing stores moved into the sales district but the other explanatory variables did not change, what would you expect for the corresponding change in annual net sales? (Use 2 decimal places.)

If you increased the local advertising by 9 thousand dollars but the other explanatory variables did not change, what would you expect for the corresponding change in annual net sales? (Use 2 decimal places.)

(f) Suppose you and your business associates rent a store, get a bank loan to start up your business, and do a little research on the size of your sales district and the number of competing stores in the district. If x2 = 2.8, x3 = 250, x4 = 3.1, x5 = 7.3, and x6 = 2, use a computer to forecast x1 = annual net sales and find an 80% confidence interval for your forecast (if your software produces prediction intervals). (Use 2 decimal places.)

forecast194.41

lower limit

upper limit

(g) Construct a new regression model with x4 as the response variable and x1, x2, x3, x5, and x6 as explanatory variables. (Use 2 decimal places for the intercept, 4 for x1, 5 for x3, and 3 otherwise.)

x4 = 4.14 + .0431 x1 + -.800 x2 + .00059x3 + -.661 x5 + Correct: .057 x6

Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, x3 = 188, x5 = 6.6, and x6 = 10. Use these data to predict x4 (advertising costs) and find an 80% confidence interval for your prediction. (Use 2 decimal places.)

prediction

lower limit

upper limit

At the 80% confidence level, what range of advertising costs do you think is appropriate for this store? (Round to nearest integer.)

lower limit $

upper limit $

Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged plus to find a job. The data on number of weeks spent searching for a job contained in the table below.

1 31 48 3 8 30 34 13 15 35 8 6 44 29 16 20 4 27 22 14 18 17 14 40 17 7 48 45 9 24 9 11 39 11 5 51 16 28 1 40

a. Provide a point estimate of the population mean number of weeks it takes a worker aged plus to find a job. Round the answer to two decimal places. weeks

b. At confidence, what is the margin of error? Round the answer to four decimal places.

c. What is the confidence interval estimate of the mean? Round the answers to two decimal places. ,

d. Find the skewness. Round the answer to four decimal places

Consider the following hypothesis test:

H₀: p ≥ 0.75
H_a: p < 0.75

A sample of 400 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use α = .05.

Round your answers to four decimal places.

a. p = 0.66

p-value

Conclusion:
p-value Select greater than or equal to 0.05, reject, greater than 0.05, do not reject, less than or equal to 0.05, reject, less than 0.05, reject, equal to 0.05, do not reject, not equal to 0.05, do not reject H₀

b. p = 0.75

p-value

Conclusion:
p-value Select greater than or equal to 0.05, reject, greater than 0.05, do not reject, less than or equal to 0.05, reject, less than 0.05, reject, equal to 0.05, do not reject, not equal to 0.05, do not reject H₀

c. p = 0.71

p-value

Conclusion:
p-value Select greater than or equal to 0.05, reject, greater than 0.05, do not reject, less than or equal to 0.05, reject, less than 0.05, reject, equal to 0.05, do not reject, not equal to 0.05, do not reject H₀

d. p = 0.76

p-value

Conclusion:
p-value Select greater than or equal to 0.05, reject, greater than 0.05, do not reject, less than or equal to 0.05, reject, less than 0.05, reject, equal to 0.05, do not reject, not equal to 0.05, do not reject

Show all working.

Use the following data to:
a) draw a scatter plot
b) find the coefficient of correlation and test the significance at the 0.05 level
c) find the regression line
d) predict y' for x = 5

Number of alcoholic drinks - x            Score on a Dexterity Test - y
              2                                                    15
                1                                                    18
                3                                                   11
                4                                                     7
                2                                                    10
                1                                                    16
                5                                                    4
                6                                                     2

A company is developing a new high performance wax for cross country ski racing. In order to justify the price marketing​ wants, the wax needs to be very fast.​ Specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion. To test​ it, the champion will ski the course 8 times. The​ champion's times​ (selected at​ random) are

58.9​,

64.3​,

45.6​,

52.1​,

45.2​,

49.9​,

54.9​,

and

44.3

seconds to complete the test course. Should they market the​ wax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Use 0.05 as the​ P-value cutoff level.

Calculate the​ P-value.

​P-value=

An institute reported that 60​% of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members.

b. The probability is 90​% that the sample percentage will be contained within what symmetrical limits of the population​ percentage? The probability is 90​% that the sample percentage will be contained above nothing​% and below nothing​%.

Although studies continue to show smoking leads to significant health problems, 20% of adults in the United States smoke. Consider a group of 280 adults.

If required, round your answers to four decimal places.

a. What is the expected number of adults who smoke?

b. What is the probability that fewer than 40 smoke?

c. What is the probability that from 35 to 70 (inclusive) smoke?

d. What is the probability that 70 or more smoke?

Construct a confidence interval of the population proportion at the given level of confidence.

x equals=860​,

n equals=1200​,

90​% confidence

What are the upper and lower bounds

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample of 31 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the filler’s initial setup will be readjusted. (a) The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test. H0 : μ 16 versus Ha : μ 16 (b) Suppose that Crown Bottling Company decides to use a level of significance of α = 0.01, and suppose a random sample of 31 bottle fills is obtained from a test run of the filler. For each of the following four sample means— x⎯⎯ = 16.05, x⎯⎯ = 15.98, x⎯⎯ = 16.03, and x⎯⎯ = 15.90 — determine whether the filler’s initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that σ equals .1. (Round your z to 2 decimal places and p-value to 4 decimal places and CI to 3 decimal places.) x⎯⎯ = 16.05 z p-value CI [ , ] x⎯⎯ = 15.98 z p-value CI [ , ] x⎯⎯ = 16.03 z p-value CI [ , ] x⎯⎯ = 15.90 z p-value CI [ , ]

Give and example of a real life situation that includes: DATA STATISTIC PARAMETER How does the statistic and the parametere differ?

Based on experience, you believe that less than 15% of the population of your city dislike the taste of cilantro. Two-hundred people were randomly selected from your city and questioned about their like or dislike of the taste of cilantro. Thirty-two of those questioned stated they disliked the taste of cilantro.

Complete the tasks and answer the questions.

• Use the 2SD method to estimate the true proportion of the population of your city that dislikes the taste of cilantro. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.
• Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with a 95% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.
• Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with an 88% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.