Question

Q: The mars company claims that 13 percent of M&Ms plain candies distributed into bags are brown. Investigate this claim with an appropriate hypothesis test. Use a significance level of a= 0.05

Color	Count
Brown	33
Non-Brown	242
Total	275

1. The p-value for this test statistic is: _______________.

2. Null Hypothesis:

3. Alternative Hypothesis:

4. Conclusion: We REJECT/DO NOT REJECT the null hypothesis. (Circle the correct answer) State what this conclusion means in terms of the problem.

5. Would it be more likely the null hypothesis is rejected for an individual bag of M&M’s, or when we poolthe class results together? Explain your answer.

Answer 1

1. The p-value for this test statistic is: 0.6219

Solution:

Here, we have to use one sample z test for population proportion.

2. Null Hypothesis:

Null hypothesis: H₀: The percentage of brown M&Ms plain candies in bag is 13%.

3. Alternative Hypothesis:

Alternative hypothesis: H_a: The percentage of brown M&Ms plain candies in bag is not 13%.

H₀: p = 0.13 versus H_a: p ≠ 0.13

This is a two tailed test.

We are given α = 0.05

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 33

n = sample size = 275

p̂ = x/n = 33/275 = 0.12

p = 0.13

q = 1 – p = 0.87

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.12 – 0.13) / sqrt(0.13*0.87/275)

Z = -0.4931

P-value = 0.6219

(by using z-table)

4. Conclusion:

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that 13 percent of M&Ms plain candies distributed into bags are brown.

5. Would it be more likely the null hypothesis is rejected for an individual bag of M&M’s, or when we pool the class results together?

Yes, it would be more likely the null hypothesis is rejected for an individual bag of M&M’s than when we pool the class results together, because the sample size for individual bag would be less. If we consider pooled results, then this will follow sampling distribution of the sample proportions.