John purchases a bag of marbles and observes and counts their colors. The bag contains 142 marbles of which 11 are orange. Use the critical value method and a 7% significance level to test the claim that the percentage of orange marbles is at most 11%.
How many populations are being tested?
Claim: The percentage of orange marbles is at most 11%.
The null and alternative hypothesis is
H0: P 0.11
H1: P > 0.11
Level of significance = 0.07
Sample size = n = 142
x = 11
Test statistic is
Critical value = 1.48
( From z table)
Test statistic | z | < Critical value we fail to reject the null hypothesis.
Conclusion:
The percentage of orange marbles is at most 11%.
142 populations are being tested.
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