Question

1. A cookie company makes cookies in 6 shapes and in the following proportions: circle 30%, oval 20%, square 15%, rectangle 15%, triangle 10% and hexagon10%. You open boxes of cookies and sort the first 100 cookies. Assume the boxes are filled randomly with the different shape.

Color	circle	oval	square	rectangle	triangle	hexagon
# of cookies	25	17	17	10	16	15

Determine whether this distribution is consistent with company’s stated proportions.

1. What is the null hypothesis?
2. What is the alternative hypothesis?
3. Enter the observed number of times a color comes up in your testing and the expected number of times that the color should come up into the X-squared goodness of fit applet.

http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/goodness.htm

4. What is the number of degrees of freedom?
5. What is the p-value? Provide a screen shot of your answer.
6. Using a 90% confidence interval, should you accept or reject the null hypothesis?
7. Does your sample support or contradict the company’s stated proportions?

Answer 1

Let the stated proportion of cookies in 6 shapes be

a) The null hypothesis is

b) The alternative hypothesis is

c) First 100 cookies were sorted. The expected number of times a color should come up is obtained by multiplying the proportion by 100. For example the expected number of cookies in shape of a circle should be 0.30*100=30.

The following table shows the observed and expected number of cookies of each shape

Color/shape	circle	oval	square	rectangle	triangle	hexagon
Observed # of cookies	25	17	17	10	16	15
Expected # of cookies	100*0.30=30	100*0.20=20	100*0.15=15	100*0.15=15	100*0.10=10	100*0.10=10

We enter these values in the applet

d) The number of groups (number of shapes) is 6. The degrees of freedom is 6-1=5

ans: The number of degrees of freedom = 5

e) We enter the degrees of freedom and hit calculate

ans: The p-value = 0.097

f) 90% confidence interval indicates a significance level

We will reject the null hypothesis if the p-value is less than the significance level.

Here, the p-value=0.097 and it is less than the significance level . Hence we will reject the null hypothesis.

g) We conclude that, at 0.10 level of significance, the sample contradicts the company's stated proportions.