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Chapter 9: Q.68 (page 541)

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is 鈥渢he drug is unsafe.鈥� What is the Type II Error?

a. To conclude the drug is safe when in, fact, it is unsafe.

b. Not to conclude the drug is safe when, in fact, it is safe.

c. To conclude the drug is safe when, in fact, it is safe.

d. Not to conclude the drug is unsafe when, in fact, it is unsafe.

Short Answer

Expert verified

Type I error for the drug is safe: One thinks the drug is safe when, in fact, it really is not.

Type II error for the drug is not safe: One thinks the drug is not safe when, in fact, it really is.

Step by step solution

01

Introduction

Statistics main purpose is to verify or disprove a notion.

For example, you might conduct research and discover that a particular medicine is useful in the treatment of headaches.

No one will believe your findings if you can't repeat the experiment.

In statistical hypothesis testing, a type I error occurs when a null hypothesis is rejected when it is true.

The type II error arises when the null hypothesis is accepted even when it is false.

02

Explanation Part a

We are given H0The drug is unsafe. Therefore, the null hypothesis state that the drug is unsafe.

Rejecting the null hypothesis H0when it is true is defined as a Type I error.

The Type I error is: One thinks the drug is safe when, in fact, it really is not.

Failing to reject the null hypothesis when it is false is defined as a Type II error.

The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

Hence, option a is incorrect.

03

Explanation Part b

Type II error occurs when the null hypothesis is accepted (not rejected) even when it is false. The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

Since option b accepts the null hypothesis even when it is false.

04

Explanation Part c

The Type I error is: One thinks the drug is safe when, in fact, it really is not.

The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

The option says that drug is safe even if it is actually safe, which defines none of the type I or type II error.

Hence, option c is incorrect.

05

Explanation Part d

The Type I error is: One thinks the drug is safe when, in fact, it really is not.

The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

The option "d" says that drug is unsafe even if it is actually unsafe, which defines neither of the type I or type II error.

Hence, option d is incorrect.

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Most popular questions from this chapter

A recent survey in theN.Y. Times Almanac indicated that 48.8%of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that142owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization

thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they

spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

The null and alternative hypotheses are:

a.Ho:x炉=4.5,Ha:x炉>4.5b.Ho:渭鈮�4.5,Ha:渭<4.5c.Ho:渭=4.75,Ha:渭>4.75d.Ho:渭=4.5,Ha:渭>4.5

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. At a 1% level of significance, an appropriate conclusion is:

a. There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.

b. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is more than 20%.

c. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.

d. There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%.

The mean entry level salary of an employee at a company is $58,000. You believe it is higher for IT professionals in the company. State the null and alternative hypotheses.

"Macaroni and Cheese, please!!" by Nedda Misherghi and Rachelle Hall

As a poor starving student I don't have much money to spend for even the bare necessities. So my favorite and main staple food is macaroni and cheese. It's high in taste and low in cost and nutritional value.

One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! \(2.02!!!Can you believe it? It made me stop and think. The world is changing fast. I had thought that the mean cost of a box (the normal size, not some super-gigantic-family-value-pack) was at most \)1, but now I wasn't so sure. However, I was determined to find out. I went to 53of the closest grocery stores and surveyed the prices of macaroni and cheese. Here are the data I wrote in my notebook:

Price per box of Mac and Cheese:

鈥� 5stores @\(2.02

鈥�15stores @\)0.25

鈥� 3stores @\(1.29

鈥� 6stores @\)0.35

鈥� 4stores @\(2.27

鈥� 7stores @\)1.50

鈥� 5stores @\(1.89

鈥� 8stores @0.75.

I could see that the cost varied but I had to sit down to figure out whether or not I was right. If it does turn out that this mouth-watering dish is at most\)1,then I'll throw a big cheesy party in our next statistics lab, with enough macaroni and cheese for just me. (After all, as a poor starving student I can't be expected to feed our class of animals!)
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