Occasionally, warning flares of the type contained In most automobile emergency kits fall 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 Ho: p = 0.10 and H,: p > 0.10, where p represents the actual proportion of defective flares made by this manufacturer. If Ho is rejected, charges of false advertising will be filed against the manufacturer. (a) Explain why the alternative hypothesis was chosen to be H,: p > 0.10. The alternative hypothesis H.: p > 0.10 was chosen because the consumer group is carrying out the hypothesis test to see if there is strong evidence in favor of the proportion of defective flares being greater than 0.10. The alternative hypothesis H,: p > 0.10 was chosen because the consumer group is carrying out the hypothesis test to see if there is strong evidence in favor of the proportion of defective flares being equal to 0.10. The alternative hypothesis H,: p > 0.10 was chosen because the consumer group is carrying out the hypothesis test to see if there Is strong evidence In favor of the proportion of defective flares being less than 0.10. The alternative hypothesis Ha: p > 0.10 was chosen because the consumer group is carrying out the hypothesis test to see if there is strong evidence in favor of the proportion of defective flares being different from 0.10. (b) Complete the last two columns of the following table. (Hint: See Example 10.7 for an example of how this is done.) Error Definition of Error Description of Error In Context Consequence of Error Conclude that the proportion of defective flares is greater than 0.1 when it really is 0.1 or less. You are not convinced that the proportion of defective flares is less The consumer group incorrectly files charges of false advertising than 0.1 when it really is less than 0.1. against the manufacturer. Type I error Reject a true Ho Conclude that the proportion of defective flares is less than 0.1 The consumer group does not file charges of false advertising against when it really is 0.1 or greater. the manufacturer when they should have. You are not convinced that the proportion of defective flares is greater than 0.1 when it really is greater than 0.1. Conclude that the proportion of defective flares is greater than 0.1 when it really is 0.1 or less. You are not convinced that the proportion of defective flares is less The consumer group incorrectly files charges of false advertising Fall to reject a false than 0.1 when it really is less than 0.1. against the manufacturer. Type II error Ho O Conclude that the proportion of defective flares is less than 0.1 The consumer group does not file charges of false advertising against when it really is 0.1 or greater. the manufacturer when they should have. You are not convinced that the proportion of defective flares is greater than 0.1 when it really is greater than 0.1
