Question

A researcher claims that at least 10% of all football helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 200 helmets revealed that 24 helmets contained such defects.

a. Does this finding support the researcher’s claim? Used a fixed-level test with α = 0.01
b. Find the P-value for this test.

Answer 1

You can use a one-sample proportional z-test for your data. (Test sample proportion = 24/200 and sample size = 200) Convert all fractions to decimals. Find the critical value in the appropriate table at .01 level of significance for a two-tailed test. Compare the test statistic you calculate to the critical value from the table. If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, do not reject the null. You can draw your conclusions from there.
Note: The p-value is the actual level of the test statistic you calculate. Find using the appropriate table.