Question 6 (a) A hospital cafeteria proposes to serve 4 main entrees. For planning purposes, the manager expects that the proportions of each that will be selected by his customers will be: Selection Proportion Chicken 0.4 Roast beef 0.2 Steak 0.1 Fish 0.3 Of the first 100 customers, 44 selected chicken, 25 selected roast beef, 13 select steak, and 18 selected fish. Should the manager revise his estimates? Use α= 0.01.

(b) Five brands of orange juice are displayed side by side in several supermarkets in Hobart. It was noted that in one day, 180 customers purchased orange juice. Of these, 30 picked Brand A, 40 picked Brand B, 25 picked Brand C, 35 picked Brand D, and 50 picked Brand E. In this city, can you conclude at the 5% significance level that there is a preferred brand of orange juice? (9 marks

Compute the following probabilities using your calculator. Assume Z is a standard normal random variable. Round all answers to three decimal places.

A. P(0<Z<1.85)P(0<Z<1.85)=

B. P(−1.15<Z<0.3)=

C. P(Z>−1.3))=

D. P(0<Z<2.35)=

E. P(−1.85<Z<0.7)=

F. P(Z>−1.2)=

Suppose the random variable xx is best described by a normal distribution with μ=29μ=29 and σ=3.4σ=3.4. Find the zz-score that corresponds to each of the following xx values.

Round answers to three decimal places

(a)  x=16.2
z=

(b)  x=33.4
z=

(c)  x=17.2
z=

(d)  x=38.6
z=

Find the following probabilities for the standard normal random variable z:

Round answers to three decimal places.

(a)  P(z≤2.21)=

(b)  P(z>−2.27)=

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 8% per year, with a SD of 23%. The hedge fund risk premium is estimated at 13% with a SD of 38%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim. a-1.

Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset

In order to test the city efficiency of the 10 Toyota Prius vehicles, the following data were collected (in mpg units):

a) Compute a sample mean and a sample standard deviation for data collected.

b) Suppose that the data set in part a) is used to determine that the Toyota hybrid is more efficient than a Honda hybrid. For a random sample of 12 Honda hybrid vehicles the average consumption was estimated 47.6 mpg with the sample standard deviation s of 0.3 mpg. Use α = 0.05

I. List data assumptions.

II. State H0 and Ha.

III. Calculate the test statistic.

IV. Make decision using the p-value approach.

V. Draw conclusion.

c) Compute 95% confidence interval for the difference in mean mpgs between a Toyota hybrid and a Honda hybrid.

Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm²/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.61, and for n = 9 nonsufferers, the average output was 2.03. Let μ₁ and μ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with σ₁ = 0.3 and σ₂ = 0.4.

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

Z=

P value=

(b) What is the probability of a type II error when the actual difference between μ₁ and μ₂ is

μ₁ − μ₂ = −1.3?

(Round your answer to four decimal places.)

1. Model Summary

Analysis of Variance

The is 0.3 Correlation Coefficient <<<<<<<<<<<<<<

1. Does the Correlation Coefficient justify your answer to #22 or would you now change your answer? Why or why not? What does the Correlation Coefficient tell you about the direction and strength of the relationship between these variables?
2. Using the P value or the critical values for the Pearson coefficient Critical Values Table for Pearson Coefficient is there enough evidence to support a relationship at the 5% level of significance (α = .05) for these variables? Explain how you arrived at your answer.
3. Using the result for the Correlation Coefficient compute the Coefficient of Determination (r-squared).
4. Interpret this value…what information does this give us concerning Earnings and Dividends?

Using the extinction coefficient of 18,000 M-1cm-1, convert A_405nm data into µM of p-nitrophenol (Note the unit change from concentration to the number of moles!). Assume that the path length is 1 cm and the total volume was 4 mL

Using Excel (or similar spreadsheet program), plot µM of p-nitrophenol produced as a function of time in minutes.  Draw a line of best-fit through the initial linear region of the data set. Determine the slope of this line and enter it as your answer (without units) using decimals, not scientific notation. The "natural" units for this slope are µM/min.

In a comparison of two different weight-loss programs, obese participants were randomly assigned to one of two groups: (1) the soy group, a low-calorie group that ate only soy-based proteins, or (2) the traditional group, a low-calorie group that received 2/3 of their protein from animal products and 1/3 from plant products. One of the dependent measures collected was the amount of body fat loss as a percentage of initial body weight.

Summary data from each group based on this variable are listed below:

Soy group (treat this as μ1): N = 6, Mean = 2.3, Variance = 0.3

Traditional group (treat this as μ2): N = 6, Mean = 1.223, Variance = 0.251

Calculate the 95% confidence interval.

List the LOWER BOUND (Round to the nearest 2 decimal places):

List the UPPER BOUND (Round to the nearest 2 decimal places):

In a comparison of two different weight-loss programs, obese participants were randomly assigned to one of two groups: (1) the soy group, a low-calorie group that ate only soy-based proteins, or (2) the traditional group, a low-calorie group that received 2/3 of their protein from animal products and 1/3 from plant products. One of the dependent measures collected was the amount of body fat loss as a percentage of initial body weight.

Summary data from each group based on this variable are listed below:

Soy group (treat this as μ1): N = 6, Mean = 2.3, Variance = 0.3

Traditional group (treat this as μ2): N = 6, Mean = 1.223, Variance = 0.251

Calculate the 95% confidence interval.

List the LOWER BOUND (Round to the nearest 2 decimal places):

List the UPPER BOUND (Round to the nearest 2 decimal places):

Part V. 1. Events G and H are defined on the sample space. If P(G) = 0.3, P(H) = 0.2, and P(G ! H) = 0.1 a) Are G and H independent? Explain. __________________________________________________________________________ b) Are G and H mutually exclusive? Explain. ___________________________________________________________________________ 2. The classical probability concept applies only when all possible outcomes are ______________________. 5 3. If A is the event that I win the lottery and B is the event that I go on vacation, then P(B | A) can be described in words as the probability that ______________________________________________________________. 4. A restaurant menu has 8 main courses, 5 appetizers, 6 desserts, and 4 beverages. The number of ways that a patron can select a meal with one appetizer, one main course, one dessert and one beverage is ________________________________________________. 5. The number of 5-player basketball teams that can be formed from a group of 11 players is _______________________________________________. 6. How many ways can letters of PROBABILITY be arranged? _____________________________________________.