Question

1. A brand of mints come in various flavors. The company says that it makes the mints in the following proportions.

Flavor	Cherry	Strawberry	Chocolate	Orange	Lime
Expected %	30%	20%	20%	15%	15%

A bag bought at random has the following number of mints in it.

Flavor	Cherry	Strawberry	Chocolate	Orange	Lime
Observed	67	50	54	29	25

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 flavor comes up in your test bag and the expected number of times that the flavor should come up into the X-squared goodness of fit applet.

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 95% confidence interval, should you accept or reject the null hypothesis?
7. Does the distribution of flavors in your random bag support or contest the company’s state proportions? (yes or no)

Answer 1

(a)

H0:Null Hypothesis: This distribution is consistent with company's stated proportions.

(b)

HA Alternative Hypothesis: This distribution is not consistent with company's stated proportions.

(c)

Observed & Expected frequencies

Flavor	Observed (O)	Expected (E)
Cherry	67	67.5
Strawberry	50	45
Chocolate	54	45
Orange	29	33.75
Lime	25	33.75

(d)

The number of degrees of freedom = 5 - 1 = 4

(e)

Test statistic is calculated as follows:

Flavor	Observed (O)	Expected (E)	(O - E)2/E
Cherry	67	67.5	0.003703704
Strawberry	50	45	0.555555556
Chocolate	54	45	1.8
Orange	29	33.75	0.668518519
Lime	25	33.75	2.268518519
Total	225		=5.2962963

By Technology, (using excel)

p - value=1-CHISQ.DIST(5.2963,4,1)

p - value = 0.2582

(f)

Since p - value = 0.2582 is not less than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Correct option:

We should not reject the null hypothesis.

(g)

The sample doesnt contradicts the company's stated proportions.