Three (3) companies supply the same part. All three companies operate in-control processes for the single quality characteristic of part-length. All three companies have a mean part-length equal to 17. The "red company" has a part-length standard deviation of 0.29 for the parts they produce. The "blue company" has a part-length standard deviation of 0.37 for the parts they produce. The "green company" has a part-length standard deviation of 0.20 for the parts they produce. The part-length specification has a tolerance span from 16 to 18.

Which company is more capable of meeting the specification? Explain and support your company choice with process capability statistics.

A population with μ = 41 and σ = 4 is standardized to create a new distribution with μ =50 and σ = 10. In this transformation, a score of X = 39 from the original distribution will be transformed into a score of X = 55. True or False?

A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Miller’s stores are x1⎯⎯⎯⎯?=?$124.31x1¯?=?$124.31 and s₁= 1.23. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2⎯⎯⎯⎯?=?$106.18x2¯?=?$106.18 and s₂= 1.63.

(a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Test statistic          

(b) Calculate the critical value. (Round your answer to 2 decimal places.)

Critical value          

(c) At the 0.05 significance level, what it the conclusion?

You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes. a. Using the six-step critical value approach, at the 0.05 level of significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 25 minutes? b. At the 0.05 level of significance, use the five-step p-value approach. c. Interpret the meaning of the p-value in (b). d. Compare your conclusions in (a) and (b)

Find the most appropriate ARMA(p,q) model to the monthly average wind speed data(from Jan 1984 to Mar 2020) and predict the next nine numbers by using R. Your analysis should include stationarity checking, model identification, parameter estimation, model diagnostics, and forecasting procedures.

A study by the U.S. Energy Information Administration found that 25% of households have an income under $10, 000 of which 84.3% did not own a dishwasher. However, it was found that only 21.8% of those in the over $10, 000 income range did not own a dishwasher. Find the following:

(Note: round the answers to 2 decimal places)

i) If one household is randomly selected from each income group, determine the probability that both households will own a dishwasher?  

ii) If one household is randomly selected from the entire group, what is the probability that they own a dishwasher and have an income over $10, 000?  

iii) If one household is randomly selected from the entire group, what is the probability that they own a dishwasher?  

iv) If one household is randomly selected from the entire group, what is the probability that they either own a dishwasher or have an income over $10, 000?  

v) If one household is randomly selected from the entire group and was found to have dishwasher, what is the probability that they have an income over $10, 000?  

vi) Are the events ‘Owing a dishwasher’ and ‘having an income over $10, 000' independent? (Insert either YES or NO as your answer)

You are given:
(iv) The claim frequency for a single insured follows a Poisson distribution with mean ?.
(v) The claim frequency rate, ?, has a gamma distribution with mean 1/10
and variance 4/10000
.
(vi) During the last 3 years, 150 claims have occurred.
(vii) In each of the three years, 200 policies were in force.
Determine the Bayesian estimate of the posterior claim frequency rate based upon the latest
observation.

1) In a two-way ANOVA, what are main effects?

2) In a two-way ANOVA, what are interaction effects?

A beer industry association is interested in determining the preference of workers for light, dark, and regular beers. A survey was conducted in which 300 blue color workers and 300 white color workers, randomly selected from two groups, were given a choice of three different beers. Each worker expressed their favorite. The following results were obtained:

The value of the chi-square test statistic is:

The critical value of chi-square obtained from the table (or using MS Excel) for a 5% level of significance (alpha) is:

Based on your answers to the previous questions, your decision is to Accept H₀. (True or False):

An operator walks from her workstation to a set of shelves 10 steps away. She picks up both a hammer (weighs 2.5 pounds) and a box of nails from the shelf(s), which are at knee level. She must reach 10 inches into the shelf to grasp the hammer. Following the retrieval of the hammer she much reaches 10 inches into an adjacent shelf to grasp a box of nails. She returns to her workstation and sets the hammer and nails down on the work surface (waist height).

Develop a MOST sequence model to describe this work activity. Calculate the estimated standard time (in seconds) for this activity

Motion and time study for lean manufacturing

A manufacturer of kitchen appliances is preparing to set the price on a new blender. Demand is thought to depend on the price and is represented by the model

D = 2,500 – 3P

The accounting department estimates that the total cost can be represented by

C = 5,000 + 5D

Develop a mathematical model for the total profit in terms of the price, P. (Using Excel)

A mail-order catalog firm designed a factorial experiment to test the effect of the size of a magazine advertisement and the advertisement design on the number of catalog requests received (data in thousands). Three advertising designs and two different-size advertisements were considered. The data obtained follow.

Use the ANOVA procedure for factorial designs to test for any significant effects due to type of design, size of advertisement, or interaction. Use α = 0.05.

Find the value of the test statistic for type of design. (Round your answer to two decimal places.)

Find the p-value for type of design. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of design.

Because the p-value ≤ α = 0.05, type of design is not significant.Because the p-value > α = 0.05, type of design is not significant.    Because the p-value > α = 0.05, type of design is significant.Because the p-value ≤ α = 0.05, type of design is significant.

Find the value of the test statistic for size of advertisement. (Round your answer to two decimal places.)

Find the p-value for size of advertisement. (Round your answer to three decimal places.)

p-value =

State your conclusion about size of advertisement.

Because the p-value ≤ α = 0.05, size of advertisement is significant.Because the p-value > α = 0.05, size of advertisement is not significant.    Because the p-value > α = 0.05, size of advertisement is significant.Because the p-value ≤ α = 0.05, size of advertisement is not significant.

Find the value of the test statistic for interaction between type of design and size of advertisement. (Round your answer to two decimal places.)

Find the p-value for interaction between type of design and size of advertisement. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between type of design and size of advertisement.

Because the p-value > α = 0.05, interaction between type of design and size of advertisement is not significant.Because the p-value ≤ α = 0.05, interaction between type of design and size of advertisement is significant.    Because the p-value > α = 0.05, interaction between type of design and size of advertisement is significant.Because the p-value ≤ α = 0.05, interaction between type of design and size of advertisement is not significant

Assume that the following pattern holds true through future generations in a certain country: 60% of the daughters of working women also work and 20% of the daughters of non–working women work. Find the transition matrix of the Markov chain modeling working/non–working states across generations.

An article investigated the consumption of caffeine among women. A sample of 43 women were asked to monitor their caffeine intake over the course of one day. The mean amount of caffeine consumed in the sample of women was 243.872 mg with a standard deviation of 209.05 mg. In the article, researchers would like to include a 90% confidence interval.   

• The values below are t critical point corresponding to 90%, 95%, 98%, and 99% confidence. Which critical point corresponds to 90% confidence?
  • 1.682
  • 2.698
  • 2.418
  • 2.018
• With 90% confidence, we estimate the mean amount of caffeine consumed by women is between  mg and  mg. (Round the limits of your interval to 4 decimal places.)
• If the level of confidence were changed to 99%, what effect would this have on the width of the calculated confidence interval?
  • the interval would narrow
  • the interval would widen
  • there would be no effect on the interval