Paint-Drying Robots Assignments

Paint-Drying Robots.

How long it takes paint to dry can have an impact on the production capacity of a business. In May 2018, Deal’s Auto Body & Paint in Prescott, Arizona, invested in a paint-drying robot to speed up its process (The Daily Courier website). An interesting question is, “Do all paint-drying robots have the same drying time?” To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained. At the level of significance, test to see 𝛼=0.05whether the mean drying time is the same for each brand of robot.

a. Use the Excel data analysis tool to perform the required test.

b. What are the null and alternative hypothesis?

c. What is the test statistic? What distribution does the test statistic follow ?

d. State your conclusions.

Consumer Preferences.

In 2018, consumer goods giant Procter and Gamble (P&G) had more than 20 brands with more than $1 billion in annual sales (P&G website). How does a company like P&G create so many successful consumer products? P&G effectively invests in research and development to understand what consumers want. One method used to determine consumer preferences is called conjoint analysis. Conjoint analysis allows a company to ascertain the utility that a respondent in the conjoint study places on a design of a given product. The higher the utility, the more valuable a respondent finds the design. Suppose we have conducted a conjoint study and have the following estimated utilities (higher is preferred) for each of three different designs for a new whitening toothpaste. At the .05 level of significance, test for any significant differences.

a. Use the Excel data analysis tool to perform the required test.

b. What are the null and alternative hypothesis?

c. What is the test statistic? What distribution does the test statistic follow?

d. State your conclusions.

Amusement Park Queues.

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use .

a. Use the Excel data analysis tool to perform the required test.

b. What are the null and alternative hypothesis?

c. What is the test statistic? What distribution does the test statistic follow?

d. State your conclusions.