Suppose that National Motors randomly selects a sample of n = 91 ZX-900s. The company records the stopping distance of each of these automobiles and calculates the mean and standard deviation of the sample of n = 81 stopping distances to be ȳ = 57.8feet and s = 6.02feet.

1. Conduct hypothesis test

H0 :μ=60, Ha :μ<60.

Set α = 0.5. And calculate the p-value.

The ages of commercial aircraft are normally distributed with a mean of 13.013.0 years and a standard deviation of 8.11428.1142 years. What percentage of individual aircraft have ages between 1010 years and 1616 ​years? Assume that a random sample of 8181 aircraft is selected and the mean age of the sample is computed. What percentage of sample means have ages between 1010 years and 1616 ​years?

Situation B: An independently selected sample of five men also participated in the same study. The table below shows results for the number of pounds lost by the five men and five women in the study. The researcher will use the .01 significance level to test whether (on average) the program produces different weight-loss results for men and women. You may assume that the population variances are equal (although the sample variances are not).

***Weight-loss is in pounds***

Men (sample 1): sample size- 5, sample mean- 19.2, standard dev.- 4.970

Women (sample 2): sample size- 5, sample mean- 12.6, standard dev.- 4.336

1) Choose the appropriate formula for the test statistic and find its value.

Using the “Z” table, indicate the values of Z₁ and Z₂associated with a 95% area under the normal distribution:

What percentage of Average Total Payments is less than $7,000?

What percentage of Average Total Payments should be less than $7,000 based upon the mean and standard deviation?

What percentage of Average Total Payments is less than $10,000?

What percentage of Average Total Payments should be less than $10,000 based upon the mean and standard deviation?

Please show how the answer was calculated.

Consider a 9 × 9 Sudoku, where each number appears exactly once in each row and
exactly once in each column. Assume that a list of numbers already appear in some
cells are given.
(a) (20pts) Write an optimization model for Sudoku.
(b) (10pts) Create your own initial list of numbers (1 through 9) which appear in
some cells of the table and use this as your input data to solve the optimization
problem in Part (a) using an optimization solver.

Using the Standard Normal Table. What is the probability a z-score is between -1.11 and 0.91?

In other words, what is P( -1.11 < z < 0.91)?

Use the graphical method for linear programming to find the optimal solution for the following problem.

Maximize P = 4x + 5 y

subject to 2x + 4y ≤ 12

                5x + 2y ≤ 10

and      x ≥ 0, y ≥ 0.

graph the feasible region

Jerome is creating a secret passcode for his vault. The vault uses some of the Greek alphabet –possible choices are (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?}, and can also use odd digits (1, 3, 5, 7, 9). The code will be of length 10 and selected randomly from the possible Greek letters or Roman Numerals mentioned above. a) How many possible secret passcodes can be formed of length 10? b) What is the probability that a randomly selected passcode contains only Greek letters and no numbers? c) What is the probability that the first and last position of a randomly selected passcode contains odd numbers? d) What is the probability that a randomly selected code has no repeats? e) Given that a randomly selected passcode contains only Greek letters, what is the probability that it starts and ends with the letter ??

A restaurant chain that has 3 locations in Portland is trying to determine which of their 3 locations they should keep open on New Year’s Eve. They survey a random sample of customers at each location and ask each whether or not they plan on going out to eat on New Year’s Eve. The results are below. Run a test for independence to decide if the proportion of customers that will go out to eat on New Year’s Eve is dependent on location. Use α=0.05.

Hypotheses:

H,0): The choice to go out on New Year's Eve is _____ restaurant location.

(H,1): The choice to go out on New Year's Eve is _____ restaurant location.

Enter the test statistic - round to 4 decimal places. ______

Enter the P-Value - round to 4 decimal places. ______

Can it be concluded that the choice to go out on New Year's Eve is dependent on restaurant location?

In a test of the effectiveness of garlic for lowering​ cholesterol, 43 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes ​(before−​after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 5.7and a standard deviation of 17.7Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol?

An orange juice producer buys only one kind of oranges. The amount of juice squeezed from each of these oranges is approximately normally distributed with a mean of 4.2 ounces and a population standard deviation of 1 ounce. If a sample of 100 oranges is selected:

(a) What is the probability that the average juice squeezed is less than 4.15 ounces?

(b) What is the probability that the average juice squeezed is more than 4.3 ounces?

(c) What is the probability that the average juice squeezed is between 4.15 ounces and 4.3 ounces?

(d) Do we need the Central Limit Theorem to solve (a) and (b)? Why or why not? Explain.

A recent National Science Foundation (NSF) survey indicates that more than 20% of the staff in American research and development laboratories is foreign. Results of the study have been used for pushing legislation aimed at controlling the number of foreign workers in the United States. An organization of foreign-born scientists wants to prove that the NSF survey results do not reflect the true percentage of foreign workers in the U.S. labs. The organization collects a sample of 5,000 laboratory workers in all major labs in the country and finds that 876 are foreign.

a). At 5% level of significance, is there sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories? Your conclusion must be in terms of the P-Value as well as setting up a Rejection Region. Show work.

b). Which statistical distribution should be applied in this situation and why? Explain carefully.

c). What type of error is possible and describe this error in terms of the problem.

d). Based on a 95% confidence level, what is the best case and worst case scenario regarding the percentage of foreigners in American laboratories?

e). Carefully interpret this interval estimation.

f). Using the results of part (d), explain carefully whether or not there is sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories? Explain carefully.

Suppose that a bag of scrabble tiles contains 5 Es, 4 As, 3 Ns and 2 Bs. It is my turn and I draw 4 tiles from the bag without replacement. Assume that my draw is uniformly random. Let C be the event that I got two Es, one A and one N. (a) Compute P(C) by imagining that the tiles are drawn one by one as an ordered sample. (b) Compute P(C) by imagining that the tiles are drawn all at once as an unordered sample.

1. The VA has collected the past month’s data from sixteen hospitals. The VA believed the selected hospitals were efficiently run. The objective is to derive a model based on the efficient hospitals to use to comparatively evaluate questionable hospitals. The data are: y = monthly labor spent x1 = monthly X-ray exposures x2 = monthly occupied bed days x3 = average number of days of a patient’s stay SUMMARY OUTPUT Regression Statistics Multiple R 0.9981 R Square 0.9961 Adjusted R2 0.9952 Standard Error 387.1598 Observations 16 ANOVA df SS MS

   		14896.25
   		15896.25
   		16009.25
   		16896.25
   		17986.25

1. The previous multiple regression model is significant to what level?

   		It is not significant
   		0.05
   		0.01
   		0.001
   		0.0000

1. In the VA prolem which is the most significant independent variable?

   		X-ray
   		BedDays
   		Length of stay