Question

According to Mars, Inc., 20% of all M&Ms produced are blue. One bag of 50 M&Ms represents the sample for this problem. The sample data can be used to perform a two-sided hypothesis test to test whether 20% of all M&Ms are blue.

In one bag of 50 M&Ms, there are 14 blue M&Ms. Use this data to test whether 20% of all M&Ms are blue.

Answer 1

Solution:

Given:

Claim: According to Mars, Inc., 20% of all M&Ms produced are blue.

that is: p = proportion of M&Ms are blue = 0.20

Sample size = n = 50

x = Number of M&Ms are blue = 14

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

where

thus

Step 3) Find z critical value:

Since level of significance is not given , we use level of significance =

Since this is two tailed, we find : Area =

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

Step 4) Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value =-1.96 or z  test statistic value > z critical value = 1.96 , otherwise we fail to reject H0.

That is rejection region is: z < -1.96 or z > 1.96.

Since z  test statistic value = is between z critical values: ( -1.96 , 1.96), that is z  test statistic value = does not fall in the rejection region, we fail to reject H0.

Step 5) Conclusion:

At 0.05 level of significance, we do not have sufficient evidence to reject the claim that: 20% of all M&Ms produced are blue.

that is: Mars, Inc. claim that 20% of all M&Ms produced are blue is true.