Question

Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite. A consumer group wants to investigate a claim that the proportion of defective flares made by a particular manufacturer is higher than the advertised value of 0.10. A large number of flares will be tested, and the results will be used to decide between:

a)H0: p > 0.10.
b)H0: p = 0.10.
c)H0: p < 0.10.
d)H0: p ≠ 0.10.

Answer 1

The consumer group should use the null hypothesis H0: p = 0.10 to test if the proportion of defective flares is higher than the advertised rate. If the p-value is lower than the significance level, the hypothesis that the defect rate is as advertised is rejected.

Step-by-step explanation:

The consumer group investigating the flare manufacturer's claims would start with the null hypothesis (H0) that the proportion of defective flares, denoted p, is equal to the advertised value of 0.10. Therefore, the correct null hypothesis to be tested is H0: p = 0.10. The alternative hypothesis (Ha) would be that p > 0.10, suggesting that the defective rate is higher than advertised. When conducting the hypothesis test, if the calculated p-value is lower than the significance level (α, also known as alpha), the null hypothesis is rejected.

For example, in your given information, if α is set to 0.05 and the obtained p-value is less than α, the decision is to reject the null hypothesis. This indicates that there is sufficient evidence at the 5 percent significance level to conclude that the proportion of defective flares is greater than 0.10. If, on the other hand, the p-value were greater than α, we would not reject the null hypothesis, indicating insufficient evidence to say the defect rate is higher than the advertised 0.10.