Investigating Defective Flares: A Consumer Group's Mission

How can a consumer group determine if the proportion of defective flares is higher than advertised?

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. What hypothesis should they use to test this claim?

Answer:

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.

When a consumer group suspects that the manufacturer's claim of a defect rate being equal to or less than 0.10 is false, they can conduct a hypothesis test to verify this claim. By setting up the null hypothesis as H0: p = 0.10, where p represents the proportion of defective flares, the consumer group can determine if there is enough evidence to reject this null hypothesis and accept the alternative hypothesis (Ha) that p is greater than 0.10.

During the hypothesis test, the consumer group will collect a large number of flares to test for defects. The results obtained will be used to calculate a p-value, which is compared to the significance level (α) set by the group. If the p-value is lower than α, typically at a significance level of 0.05, the null hypothesis is rejected, indicating that there is enough evidence to support the claim that the defect rate is higher than 0.10.

It is crucial for the consumer group to follow proper statistical procedures in conducting this investigation to ensure accurate and reliable results. By using the correct hypothesis testing methods, the group can make an informed decision on the manufacturer's claim about the defect rate of the flares.