A company with a large fleet of cars found that the emissions systems of 18 out of the 65 randomly selected cars they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Test the appropriate hypothesis and carefully state your conclusion. Make sure you include the two hypotheses, check the conditions, give the test statistic and the p-value before you write your conclusion using first 5% significance level, then write your conclusion using 10% significance level.

Answer 1

Here are a few steps to get you started:

Null hypothesis:
Ho: p = .20 -->meaning: population proportion is equal to .20
Alternative hypothesis:
Ha: p > .20 -->meaning: population proportion is greater than .20

Using a formula for a binomial proportion one-sample z-test with your data included:
z = .277 - .20 -->test value (18/65 is approximately .277) minus population value (.20)
divided by
√[(.20)(.80)/65]

Finish the above calculation. To find p-value, use a z-table. (P-value is the actual level of the test statistic.)

If the test statistic exceeds the critical value you find in the z-table for a one-tailed test (the test is one-tailed because the alternative hypothesis is showing a specific direction), reject the null and accept the alternative hypothesis. If the test statistic does not exceed the critical value from the table, do not reject the null. You can draw your conclusions using the two significance levels stated in the problem.

I hope this will help.

Answer 2

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