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Chapter 9: Q. 11 (page 537)

The mean price of mid-sized cars in a region is $32000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.

Short Answer

Expert verified

Type I error: The mean price of mid-sized automobiles is $32,000, when it is $32,000.

Type II error: The average price of a mid-sized car is not $32,000, whereas it is actually $32,000.

Step by step solution

01

Given information

The mean price of mid-sized cars in a region is$32000.

02

Explanation

There are four possible results when running a hypothesis test, based on the veracity (or falseness) of the null hypothesis H0and the decision to reject or not.

1. When H0is true, the decision is not to reject it.

2. If H0is true, the decision is to reject it.

3. The decision is to not reject H0even though it is false.

4. If H0is untrue, the decision is to reject it.

Type I error: The mean price of mid-sized automobiles is $32000, when it is $32,000.

Type II error: The average price of a mid-sized car is not role="math" localid="1653549384021" $32,000, whereas it is actually role="math" localid="1653549390631" $32,000.

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Most popular questions from this chapter

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

For statements a-j ( Section: 9.109 ), answer the following in complete sentences.

a. State a consequence of committing a Type I error.

b. State a consequence of committing a Type II error.

"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!)

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. At a significance level of a = 0.05, what is the correct conclusion?

a. There is enough evidence to conclude that the mean number of hours is more than 4.75

b. There is enough evidence to conclude that the mean number of hours is more than 4.5

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

"The Craven," by Mark Salangsang

Once upon a morning dreary

In stats class I was weak and weary.

Pondering over last night鈥檚 homework

Whose answers were now on the board

This I did and nothing more.

While I nodded nearly napping

Suddenly, there came a tapping.

As someone gently rapping,

Rapping my head as I snore.

Quoth the teacher, 鈥淪leep no more.鈥�

鈥淚n every class you fall asleep,鈥�

The teacher said, his voice was deep.

鈥淪o a tally I鈥檝e begun to keep

Of every class you nap and snore.

The percentage being forty-four.鈥�

鈥淢y dear teacher I must confess,

While sleeping is what I do best.

The percentage, I think, must be less,

A percentage less than forty-four.鈥�

This I said and nothing more.

鈥淲e鈥檒l see,鈥� he said and walked away,

And fifty classes from that day

He counted till the month of May

The classes in which I napped and snored.

The number he found was twenty-four.

At a significance level of 0.05,

Please tell me am I still alive?

Or did my grade just take a dive

Plunging down beneath the floor?

Upon thee I hereby implore.
See all solutions

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