Week 11 - Application Assignment

Part 1) M&M Color Distribution (5 points)

The Mars Company, makers of M&M candy, claims that in every plain M&M bag there is 13 % redpieces, 14% yellowpieces, 16% greenpieces, 20% orange pieces, 24% bluepieces, and 13% brownpieces. The company also states thatthe colors are blended mechanically according to the formula, but occasionally an unusual assortment of colors may appear.

Aisha got a 32 oz bag of M&M and sorted the pieces according to their colors. She recorded the counts below. She wants to see if her bag of M&Ms follows the claimed color distribution of the Mars Company.

	Red	Yellow	Green	Orange	Blue	Brown	Total
Observed counts of M&M pieces for each color	130	149	155	210	252	123	1019
Expected number of M&M pieces for each color

1. What type of hypothesis test is required here?State all assumptions required for this test.

1. Fill in the row of expected values in the table above. Round each value to 1 decimal place.

1. State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

1. Using = 0.10, run the correct hypothesis test and provide the information below. Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

Test Statistic

Critical value [HINT: this is NOT ]

Degrees of Freedom

p-value

1. State your statistical decision (and justify it!) and interpret your decision within the context of the problem. What is your conclusion?

Part 2) GIRL SCOUT COOKIES (5 points)

You are contacted by the top cookie-selling Girl Scout troop in the city. As part of their sales plan for next year's cookie selling season, they need to know (with 99% confidence, or = 0.01) if the types of cookies purchased by their customers depends on where the scouts sell them. Here is their confidential sales data from last year:

		Type of Cookie Sold
		Thin Mints	Tagalongs	Do-si-dos	Trefoils	Samoas
Sales Method	At parents' workplace	472	641	358	327	351
Door-to-Door	840	1092	673	511	542
Community Events	683	742	491	420	374

1. What type of hypothesis test is required here?State all assumptions required for this test.

1. State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

1. Run the correct hypothesis test and provide the information below. Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

Test Statistic

Critical value [HINT: this is NOT ]

Degrees of Freedom

p-value

1. Fill-in the Expected Values of each cell below. Round answers to 2 decimal places.

(Hint: Use the output of the statistical test you ran above found in Matrix B!)

		Type of Cookie Sold
		Thin Mints	Tagalongs	Do-si-dos	Trefoils	Samoas
Sales Method	At parents' workplace
Door-to-Door
Community Events

1. State your statistical decision (and justify it!) and interpret your decision within the context of the problem. What is your conclusion?

Part 3) Life Expectancy of Countries (6 points)

Review the Health data given in the Excel spreadsheet. The variable of Infant Mortality is the number of infant deaths in thousands in that country, and the Life Expectancy is the average number of years a person lives in that country.

1. Create a scatterplot to see the relationship between the variables Infant Mortalityand Life Expectancy.Copy and paste your graph here. What is the independent variable? Dependent variable?

1. Find the correlation coefficient, r and describe the relationship between Infant Mortality and Life Expectancy.Round your answer to 3 decimals.

1. Find the equation of the estimated linear regression line. Write the equation below and sketch it on the scatter plot.

1. What percent of the variation in the dependent variable can be explained by this linear relationship? What is this number called?

1. If the number of infant deaths in a country is 50 (thousands), what would you predict the Life Expectancy of that country to be? (Use the estimated linear regression line in question 3)

1. If the Life Expectancy of a country is 67 years, what would you expect the number ofInfant Mortalityof that country to be? (Use the estimated linear regression line in question 3)