Taste the Rainbow - Lab PDF

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Lab...

Description

The original Skittles Brand candies come in red, orange, yellow, green, and purple (violet). It is well know that M&M Brand candies are not represented with equal frequency. However, do the colors of Skittles candies occur with equal frequency? For this lab you will need a bag of skittles candies as shown below. This bag is the 2.17 oz (61.5 g) bag available at most candy counters.

My Data Results Red- 12 Orange-13 Yellow-10 Green-12 Purple-12 1. Write the appropriate null and alternative hypothesis to determine if the proportion of each color is the same in a bag of Skittles.

Ho :

p=0.2

versus

H1 : p≠0.20

Null hypothesis: The probability of getting each colored skittle is the same as getting any other skittle color. Alternative hypothesis: The probability of getting each colored skittle is not the same as getting any other of each color. Randomly choose a color from one of the five colors. Count the total number of candies in the bag as ˆ , for the color you well as the number for the color you selected. What is the sample proportion, p chose?

Number of Skittles in the bag: 59

Number of Skittles in your color: Red- 12 ˆ , for your color:12/59=0.20338=0.20 Sample proportion, p

2.

Treat the candies in the bag as a simple random sample of all original Skittles candies produced. Verify the model requirements to conduct an appropriate hypothesis test. (For the purposes of this lab, verification means that you have at least 5 Skittles Candies in your color choice and at least 5 not in your color choice.)

Hypothesis Testing= Conditions of hypothesis testing must have at least 5 Skittles Candies in your color choice and at least 5 not in your choice in the sample, therefore; the trials are independent, simple random population, and the sample size must be 10% or smaller than the population size. Also, np(1-p) ≥10. In doing so, I am able to calculate if Ho is rejected or if it is failed to be rejected based on the sufficient evidence. I will use the P-value approach( a two tailed test) to conclude my results and what I find. 0.05 significance level to test the claim that 20% of all skittles candies are red and that anything other than red will be present in the bag. np(1-p) ≥10 sample random sample of all original Skittle candies produced 59(0.5)(1-.50) ≥10 14.75≥10

3.

Test the hypothesis you wrote in step #1 of the Skittles Lab by doing the following. (a) State the null hypothesis and (b) the alternate hypothesis, (c) State the type of test that you will use to test the hypothesis and the level of significance, (d) state the critical-z value(s), (e) state the z-statistic, (f) state the relation between the p-value and α with an appropriate inequality (g) state whether we shall reject or fail to reject the null hypothesis, and (h) conclude the hypothesis test with an appropriate in context summarizing statement that address what we shall do with the alternate hypothesis.

a)

H0: p = 0.2, H1: p ≠ 0.2

b)

I will use the P-value approach (a two-tailed test), with α = 0.05

c.) Critical Z-Value: ± 1.645

d)

Z-statistic = -0.645

e)

f)

P value = 0.09997 > α

We fail to reject the null hypothesis

g) Since the P value is greater than α, we fail to reject the null hypothesis. There is not sufficient evidence at the α = 0.05 level to conclude that anything other than 0.2 Skittles of one color (red, in this case) will be present in a bag.

4. Post your results to question 4 in the discussion board entitled “Taste the Rainbow.” Respond to the prompts in the Discussion Board....