In: Statistics and Probability
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.
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%.