Eco Hw 8
1. An article in Marketing News argued that the level of significance used when comparing two products is often too low – that is, sometimes you should be using an α value greater than 0.05. Specifically, the article recounted testing the proportion of potential customers with a preference for product 1 over product 2. The null hypothesis was that the population proportion of potential customers preferring product 1 was 0.50 and the alternative hypothesis was that it was not equal to 0.50. the p-value for the test was 0.22. the article suggested that, in some cases, this should be enough evidence to reject the null hypothesis.
a. State the null and alternative hypotheses for this example in statistical term
Null hypothesis: The population proportion of customers preferring product 1 is 0.50.
Alternative: The proportion of customers preferring product 1 is not equal to 0.50.
b. Explain the risk associated with Type I and Type II errors in this case.
The risk with these errors are that you will reject the hypotheses when they are true.
c. What would be the consequences if you rejected the null hypothesis for a p-value of 0.22?
There will not be enough evidence to reject the null hypothesis
d. Why do you think the article suggested raising the value of α?
To decrease the chance for type I or type II errors
e. What would you do in this situation?
Keep the a value the same
f. What is your answer in (e) if the p-value equals 0.12? what if it equals 0.06?
I would probably in crease the a value for the p value of 0.06 because it is so close, there is a greater chance of our rejecting the null hypothesis to be an error.
2. A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing the number of pounds of force applied to
a. State the null and alternative hypotheses for this example in statistical term
Null hypothesis: The population proportion of customers preferring product 1 is 0.50.
Alternative: The proportion of customers preferring product 1 is not equal to 0.50.
b. Explain the risk associated with Type I and Type II errors in this case.
The risk with these errors are that you will reject the hypotheses when they are true.
c. What would be the consequences if you rejected the null hypothesis for a p-value of 0.22?
There will not be enough evidence to reject the null hypothesis
d. Why do you think the article suggested raising the value of α?
To decrease the chance for type I or type II errors
e. What would you do in this situation?
Keep the a value the same
f. What is your answer in (e) if the p-value equals 0.12? what if it equals 0.06?
I would probably in crease the a value for the p value of 0.06 because it is so close, there is a greater chance of our rejecting the null hypothesis to be an error.
2. A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing the number of pounds of force applied to