The following data is based on information taken from Winter Wind Studies in Rocky Mountain National Park by D. E. Glidden (Rocky Mountain Nature Association). At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below:

Does this information indicate that peak wind gusts are higher in January than in April? Use a .03 significance level. Please use the four step process and round your answers to the nearest fourth decimal place.

A) Distinguish between nonprobability and probability samples and compare their advantages and disadvantages.

Which are used for qualitative and which for quantitative studies?

1) Identify and describe two types of non-probability sampling methods and two types of probability sampling methods

2) Discuss how sample size requirements differ between qualitative and quantitative studies.

B) Identify phenomena/variables that lend themselves to self-reports, observation, and biophysiologic measurement and discuss each of these types of data collection.

A simple random sample of 60 items resulted in a sample mean of 69. The population standard deviation is 17.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

( , )

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

( , )

c. What is the effect of a larger sample size on the margin of error?

- it increases, it decreases, it stays the same, or it cannot be determined from the given data??

Problem 16-03

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
   
   
   
2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
   
   
   
3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.
   
   miles

I’m a little confused as to when to calculate the possibility using factorial, raise to the nth power and multiplication.

For example: roll a pair of 6-sided dice and there will be 36 outcomes. In this case I assume it’s 6*6 = 36

However, when should I use 6! or 6^6?

Thank you!

What is the EVPI?

please round to 1 decimal point

An operations manager for a major airline carrier conducts an analysis of overbooked flights. The airline’s goal is to have every seat on the aircraft filled by a passenger on each flight. Based on historical data, the airline estimates that 80% of the individuals that have a ticket for a particular flight actually board that flight. In order to compensate for the no shows, the airline overbooks each flight. If the number of individuals with a ticket at the gate exceeds the capacity of the aircraft, the airline must offer compensation to any individual willing to surrender their ticket. The airline will continue to increase this compensation until the number of individuals with tickets equals the capacity of the aircraft. As the date of each flight approaches, the airline must determine how many tickets to sell. If a flight has 20 open seats remaining four days before the flight date, how many tickets should the airline sell in order to fill as many seats as possible while keeping the likelihood of overbooking less than 0.15?

a. What is the name of the distribution that you used to model this problem?

b.What are the values of the parameters of this distribution?

c. Find P(x>20)

.d. Based on your analysis, how many tickets should the airline sell?

Problem 16-01 (Algorithmic)

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

1. Compute profit per unit for the base-case, worst-case, and best-case.
   
   Profit per unit for the base-case: $  
   
   Profit per unit for the worst-case: $  
   
   Profit per unit for the best-case: $  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $4. Use simulation to estimate the probability the profit per unit will be less than $4. If required, round your answer to one decimal place.
   
   %

The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 42 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 22 white-collar employees worked on average 44.03 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 42? Assume that the population standard deviation is 3.09 hours. Please use the exact value (from R) for all critical values.

a) What assumptions are required so that you can perform a hypothesis tests and confidence interval for the mean hours worked per week?

b) Should you use a z distribution or a t distribution in this problem? Note that you will only get one try to get this question correct.Please explain the correct choice.

c) Is there any evidence to suggest the true mean number of hours worked per week by white-collar workers is greater than 42? Perform the hypothesis test at a 0.8% significance level.

i) Calculate the test statistic.

ii) Calculate the p-value. Please write your answer in scientific notation using an E for the exponent and including at least 3 decimal places. For example, 1.234 x 10^-5 would be written as 1.234E-5.

iii) Write the complete four steps of the hypothesis test below.

iv) Provide your computer code for part c) below.

d) Calculate the appropriate 99.2% bound that is consistent with what you did in parts b) and c).

i) Interpret the bound calculated above.

ii) Provide your computer code for part d) below.

e) In practical terms, do you think that the number of hours worked per week by white-collar workers is greater than 42? To receive credit, your answer must be more than just repeating the conclusions in parts c) and d). Please explain your answer. Hint: Difference and Effect Size.

f) Explain why parts c) and d) state the same thing. That is, what in part c) is consistent with what in part d)?

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.5 with a standard deviation of 2.2. ​(a) What response represents the 94th ​percentile? ​(b) What response represents the 59th ​percentile? ​(c) What response represents the first ​quartile?

A small study is conducted involving 10 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams.:

Gestational age: 34.7, 36, 29.3, 40.1, 35.9, 40.8, 38.3, 37, 41.2, 39.8.

Birth weight:1895, 2030, 1440, 2835, 3115, 4013, 3174, 3625, 2289, 2845.

a) Find the correlation coefficient of the gestational age at birth and birth weight.

b) Test H0:ρ= 0 vs.H1:ρ does not equal 0. at 5% level of significance. Here ρ is the population correlation coefficient between the two variables. Use P(t8>2.36) = 0.025.

c) Construct a regression lineY=β0+β1X+, where Y,X are gestational age at birth and birth weight respectively. What are the best estimates of β0 and β1?

d) Test H0:β1= 0 vs. H1:β1 not equal 0 at 5% level of significance.

e) Compute the coefficient of determination,R^2.

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature

50°C 60°C 70°C

35 33 29

25 34 34

37 37 34

40 26 36

33 30 37

Complete an ANOVA table

Drugs are often used for reducing the blood pressure of hypertensive patients (those with high blood pressure). An experiment was run to investigate the effect of Drug (A or B) and Dose Level (Low or High) on the reduction in blood pressure. The experiment was conducted separately for the 36 patients who had mild hypertension and the 24 patients who had severe hypertension as the researcher suspected that results may differ for the two groups. For this design, there are:

A different teacher wants to see if Test 1 was predictive of Test 2. Please answer the following questions based on the data set.

A) What is the y intercept?

B) What is the slope?

C) What is the amount of variance explained in Test 2 by Test 1?

D) Assuming a student got an 84 on Test 1, what is the predicted score for Test 2? Please round to the nearest whole number.

E). For the Excel Data Set please find and report for Test 1 and Test 2 the Mean, SD, and the tolerance levels for both for which there would be any outliers (i.e., the value for which a score must be less than to be consider an outlier and the value for which a number must greater than to be considered an outlier.

A random sample of size n = 472 is taken from a population of size N = 9,700 with mean μ = −63 and variance σ2 = 176. [You may find it useful to reference the z table.]

A-1

Is it necessary to apply the finite population correction factor?

• Yes

• No

a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)

Expected Value-

Standard Error-

b. What is the probability that the sample mean is between −65 and −61? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)
Probability-

c. What is the probability that the sample mean is greater than −62? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability-