Chapter PV, Problem 30RE

(a)

To determine

To explain what kind of study is this.

Answer to Problem 30RE

This is an experimental study.

Explanation of Solution

It is given in the question that an auto parts company advertises that its special oil additive will make the engine "run smoother, cleaner, longer, with fewer repairs". Since the study involves the treatment of using the additive and comparing the effect of using the additive with the historical repair percentage, this is an experimental study.

(b)

To determine

To explain will they do a one-tailed or two-tailed test.

Answer to Problem 30RE

This is one-tailed test.

Explanation of Solution

It is given in the question that an auto parts company advertises that its special oil additive will make the engine "run smoother, cleaner, longer, with fewer repairs". Since the claim is that special oil additive will make the engine “run smoother and have fewer repairs, this is one-tailed test.

(c)

To determine

To explain in this context what a Type I error would be.

Explanation of Solution

It is given in the question that an auto parts company advertises that its special oil additive will make the engine "run smoother, cleaner, longer, with fewer repairs". Since the claim is that special oil additive will make the engine “run smoother and have fewer repairs, this is one-tailed test. As, we can say that null hypothesis: Special oil additive will not make the engine “run smoother, cleaner, longer, with fewer repairs and have repair percentage equal to historical repair percentage. And the alternative hypothesis: Special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs (repair percentage less than historical repair percentage).

Thus, the Type I error is Rejection of a true null hypothesis. Type I error is supporting the company's claim that Special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs but in reality, have repair percentage equal to historical repair percentage.

(d)

To determine

To explain in this context what a Type II error would be.

Explanation of Solution

It is given in the question that an auto parts company advertises that its special oil additive will make the engine "run smoother, cleaner, longer, with fewer repairs". Since the claim is that special oil additive will make the engine “run smoother and have fewer repairs, this is one-tailed test. As, we can say that null hypothesis: Special oil additive will not make the engine “run smoother, cleaner, longer, with fewer repairs and have repair percentage equal to historical repair percentage. And the alternative hypothesis: Special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs (repair percentage less than historical repair percentage).

Thus, the Type II error is accepting of a false null hypothesis. Type II error is not supporting the company's claim that Special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs but in reality, repair percentage using special additive less than historical repair percentage.

(e)

To determine

To explain which type of error would the additive manufacturer consider more serious.

Answer to Problem 30RE

Type I error is more serious.

Explanation of Solution

It is given in the question that an auto parts company advertises that its special oil additive will make the engine "run smoother, cleaner, longer, with fewer repairs". Since the claim is that special oil additive will make the engine “run smoother and have fewer repairs, this is one-tailed test. Thus, we can say from part (c) and part (d) that Type I error is more serious, as the customers believe the company's claim which is not true and will lead to customer's dissatisfaction towards the company.

(f)

To determine

To explain can the company conclude it is an effect of the additive and can they generalize this result and recommend the additive for all cars.

Answer to Problem 30RE

Yes, the company can conclude.

Explanation of Solution

It is given in the question that an auto parts company advertises that its special oil additive will make the engine "run smoother, cleaner, longer, with fewer repairs". Since the claim is that special oil additive will make the engine “run smoother and have fewer repairs, this is one-tailed test. Thus, yes, the company can conclude it is an effect of the additive and can they generalize this result and recommend the additive for all cars because it was controlled experiment and reconnecting it for all cars may not work though because taxi cabs are used more than the average car.