Question

In: Statistics and Probability

Suppose that in a random selection of 100100 colored​ candies, 2424​% of them are blue. The...

Suppose that in a random selection of

100100

colored​ candies,

2424​%

of them are blue. The candy company claims that the percentage of blue candies is equal to

2727​%.

Use a

0.050.05

significance level to test that claim.

Solutions

Expert Solution

Solution:

Given:

Claim: the percentage of blue candies is equal to 27​%.

Significance level = 0.05

Sample size = n = 100

Sample proportion of blue candies =

Step 1) State H0 and H1:

Since claim is non-directional, this is two tailed test.

Step 2) Test statistic:

Step 3) Find z critical values:

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.

Since z  test statistic value = -0.68 is neither < -1.96.nor > 1.96, we fail to reject null hypothesis.

Step 5) Conclusion:

At 0.05 significance level , we do not have sufficient evidence to reject the claim that the percentage of blue candies is equal to 27​%.


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