QUESTION (*Please provide a break down and describe the steps that show how you arrived at the solution)

Saeko has a yarn shop and wants to test her theory on what types of colors she is selling.

She believes that Black, White, the Primary Colors, and Tertiary colors sell in equal amounts.

The primary colors are blue, red, and yellow; while the tertiary colors are Brown, Green, and Purple.

Test Saeko's theory using the 5 step hypothesis testing analysis and Chi Square at the .10 level of significance.

Here is the pivot table that shows Saeko the number of yards that were sold in the various yarn types during the busiest weekend of her shop last year.

Row Labels Count of Color Type Sum of Yards

Black 23 35856

Blue 16 17053

Brown 13 13426

Green 12 12509

Purple 12 12131

Red 8 8393

White 26 37666

Yellow 12 12874

Grand Total 122 149908

1) Using the pivot table that you just created, fill in the blanks in the following table:

Primary Colors consists of the sum of Blue, Red, and Yellow yarn sold

Tertiary Colors consists of the sum of Brown, Green, and Purple Colors Sold.

The Total in this chart must equal the Grand Total in the above table.

Black ??

White ??

Primary Colors ??

Tertiary Colors ??

Total ??

This table (above) represents the observed data in the Chi Square analysis.

b) Find the Expected values for each of the colors.Saeko expects that the colors sell in equal amounts.

Color Type Sum of Yards

Black ???

White ???

Primary Colors ???

Tertiary Colors ???

Total ???

c) Subtract the Expected values from the observed values

Color Type Sum of Yards

Black ???

White ???

Primary Colors ???

Tertiary Colors ???

d) Square the values just found

Color Type Sum of Yards

Black ???

White ???

Primary Colors ???

Tertiary Colors ???

e) Divide each square by the expected value and add together

Color Type Sum of Yards

Black ???

White ???

Primary Colors ???

Tertiary Colors ???

Total ???

This total is your Chi Square test statistic

2) Use the 5 step hypothesis testing procedure to determine if Saeko's hypothesis that the colors sell in equal amounts is true.

a) What is the null hypothesis?

b) What is the alternative hypothesis?

c) What is the level of significance?

3) What is the Chi Square test statistic?

4) What is the Chi Square critical Value? Use =CHISQ.INV()

What is your answer to Saeko?