Researchers at a food company are interested in how a new ketchup made from green tomatoes (and green in color) will compare to their traditional red ketchup. They are worried that the green color will adversely affect the tastiness scores. They randomly assign subjects to either the green or red ketchup condition. Subjects indicate the tastiness of the sauce on a 20-point scale. Tastiness scores tend to be skewed. The scores follow:

Green Ketchup
14

15

16

18

16

16

19

Red Ketchup
16

16

19

20

17

17

18

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

Problem 2.22 (modified from Montgomery, 9th edition) The mean shelf life of a carbonated drink should exceed 120 days. Ten bottles are randomly selected and tested, and the results below are obtained: shelf life (days) = {108, 124, 124, 106, 115, 138, 163, 159, 134, 139} a) Clearly state the hypothesis to be tested, first in English and then in mathematical expressions for H0 and H1. b) Test the hypothesis at significance level 0.01. Report both the p-value and a 99% confidence interval to support your conclusion. Be sure to clearly state your conclusion in plain English and within the context of the problem.

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 28. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at 125)

The population proportion is .65 . What is the probability that a sample proportion will be within + or - .02 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table. a. n=100 b. n=200 c. n=500 d. n=1000 e. What is the advantage of a larger sample size? With a larger sample, there is a probability will be within + or - .02 of the population proportion .

Consider a random sample of 200 one-way commute distances (in miles) from Radcliffe College to a student’s primary place of residence. The sample mean is 10.33 miles and the sample standard deviation is 3.77 miles. What percent of students sampled live between 0.81 and 19.85 miles from Radcliffe College? Suppose a student lived 25 miles from Radcliffe College. Would this commute distance be considered an outlier?

Discuss the differences between Attributes Control Charts and Variables Control Charts and how you believe one can benefit a company/organization over the other, and why/why not.

(Note: Pleaee, the answer has to be typed, not hand written nor a picture.)

Thank you.

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? 0.61  0.78  0.10  0.88  1.27  0.56  0.91 What is the confidence interval estimate of the population mean mu​?

The following should be performed using R and the R code included in your submission.

To obtain first prize in a lottery, you need to correctly choose n different numbers from N and 1 number from 20, known as the supplementary. That is we first draw n numbers from 1:N without replacement and then 1 number from 1:20 in another draw. Suppose n=7 and N=35. Let X be the number of drawn numbers that match your selection, where the supplementary counts as 8, so that X=0,…,15. For a first prize X=15 i.e. all numbers are matched.

(a) Calculate probabilities P(X=x), x=0, 1, …, 7, without and with the supplementary. Plot the distribution function and the cumulative distribution function. Hint: Part of the answer involves the hypergeometric.

(b) Using R, generate 1,000,000 random numbers from this distribution and plot a histogram of the simulated data.

(c) Calculate the expected value, E(X), and the variance, σ2 (or Var(X)). Obtain the mean and the variance of the simulated data. Compare the estimates with the theoretical parameters.

(d) Assume that each week 10,000,000 entries are lodged, for a single draw. What is the value of � from the Poisson approximation to the number of entries with a first prize? Use the Poisson approximation for the following. What is the probability that there will be no entry with a first prize? What is the expected number of weeks until the first prize?

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H₀: μ = 20 versus H_a: μ > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)

(a)    n = 15, t = 3.3, α = 0.05
P-value =

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.  

  Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(b)    n = 9, t = 1.7, α = 0.01
P-value =

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.    

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(c)    n = 29,

t = −0.3

P-value =

State the conclusion in the problem context.

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.  

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

All logs are to base e

Size is in cubic centimeters, Age is in years, Weight is in pounds, Temperature is in degrees Fahrenheit, Height is in inches, Cost is in dollars, and Distance is in miles

The regression equation is
Log(Size) = 28.6 + 0.0292 Age - 1.124 Weight - 1.69 log(Temperature) + 1.02 log(Height) + 2.24 log(Cost) - 0.334 log(Distance)

S = 64.1788   R-Sq = 86.1%   R-Sq(adj) = 72.1%

Answer the following question using three decimals.
If the effect is not statistically significant put in NA
Put in percentages without the percent sign, so put in 10 instead of 10%

1-

As age increases by 1 year the size increases by the percentage

2 -

As weight increases by one pound the size decreases by the percentage

3-

As temperature increases by 7% the size will decrease by the percentage

4-

As Height increases by 3% the size increases by the percentage

5- As cost increases by 5% the size increases by the percentage

Time spent using​ e-mail per session is normally​ distributed, with mu equals 7 minutes and sigma equals 2 minutes. Assume that the time spent per session is normally distributed. Complete parts​ (a) through​ (d). a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 6.8 and 7.2 ​minutes?

Acme Outdoors Co. is introducing a new line of sport all-terrain vehicles (ATVs). Acme is considering program proposals from two competing companies: A & B. A's marketing plan is expected to generate high sales with a 75% probability and only a 25% likelihood of low sales.

An alternative marketing plan from company B could result in an initial 60% likelihood of high ATV sales and 40% probability of low sales. But company B's offer also contains a provision for an optional follow-on promotion if a low response is returned. If an optional follow-on ATV promotion is conducted by company B, there is a 70% chance of ultimately realizing high sales.

Draw an decision tree diagram with branches labeled and probabilities, do not solve.

“Larry’s logs” is planning to change the supplier. For complete analysis he needs to compute the Multifactor Productivity (MFP) for each supplier. He expects to produce 240 units using old supplier, and 260 using the new supplier. He pays $10 per hour, and will use 300 labor hours with current supplier and 308 hours with the new supplier. Other costs will be consistent across both suppliers (materials are $10 per log), using a total of 100 logs; capital costs will be $350 and energy $150).

What is the total cost for current and new supplier?

What is the multifactor productivity for the current and new supplier?

What is percent change in multifactor productivity?

1)    A lawn and garden retailer operates 4 stores in the DFW Metroplex. One of its most popular items is a lawn tractor. Weekly customer demand is distributed N(10,5²) at each store. Each store replenishes its stock to 15 lawn tractors at the start of each week. Note: Assume that weekly demands at each store are independent.

a)   Consider just one store. What is the probability of a stockout in that store?

b)   What is the probability of a stockout in at least two of the four stores?

c)   Suppose that the four stores decide to pool their stock. Specifically, they decide to pool their weekly allocations (4 X 15 = 60) in a centrally located warehouse and draw from it as needed to satisfy their demand. How often will a store experience a stockout now?