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Chapter 9: Q. 90 (page 547)

"Blowing Bubbles," by Sondra Prull

Studying stats just made me tense,

I had to find some sane defense.

Some light and lifting simple play

To float my math anxiety away.

Blowing bubbles lifts me high

Takes my troubles to the sky.

POIK! They're gone, with all my stress

Bubble therapy is the best.

The label said each time I blew

The average number of bubbles would be at least 22.

I blew and blew and this I found

From64blows, they all are round!

But the number of bubbles in64blows

Varied widely, this I know.

20per blow became the mean

They deviated by 6, and not16.

From counting bubbles, I sure did relax

But now I give to you your task.

Was22a reasonable guess?

Find the answer and pass this test!

Short Answer

Expert verified

The alternate hypothesis states that the mean number of bubbles is at least less than22remains true.

Step by step solution

01

Given information

The average number of bubbles each time is at least22.

Sample size=64

02

Explanation

Hypothesis:

The null hypothesis claims that the mean number of bubbles is at least22

H0:μ≥22Ha:μ<22

The random variable is X¯, the mean number of bubbles.

By using students't-distribution we get,

tn-1=t64-1=t63

The sample mean X¯=20

Calculate the Zvalue,

t=X¯-μs/nwhereμispopulationmean,nissamplesizez=X¯-μσ/n=20-226/64=-26/8=-20.75=-2.667

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Most popular questions from this chapter

A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use?

"Phillip’s Wish," by Suzanne Osorio

My nephew likes to play

Chasing the girls makes his day.

He asked his mother

If it is okay

To get his ear pierced.

She said, “No way!”

To poke a hole through your ear,

Is not what I want for you, dear.

He argued his point quite well,

Says even my macho pal, Mel,

Has gotten this done.

It’s all just for fun.

C’mon please, mom, please, what the hell.

Again Phillip complained to his mother,

Saying half his friends (including their brothers)

Are piercing their ears

And they have no fears

He wants to be like the others.

She said, “I think it’s much less.

We must do a hypothesis test.

And if you are right,

I won’t put up a fight.

But, if not, then my case will rest.”

We proceeded to call fifty guys

To see whose prediction would fly.

Nineteen of the fifty

Said piercing was nifty

And earrings they’d occasionally buy.

Then there’s the other thirty-one,

Who said they’d never have this done.

So now this poem’s finished.

Will his hopes be diminished,

Or will my nephew have his fun?

H0:p=0.5,Ha:p≠0.5

Assume the p-value is 0.2564. What type of test is this? Draw the picture of the p-value.

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α=0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

It is believed that a stock price for a particular company will grow at a rate of 5per week with a standard deviation of1. An investor believes the stock won’t grow as quickly. The changes in stock price are recorded for ten weeks and are as follows: 4,3,2, 3, 1,7, 2,1,1, 2. Perform a hypothesis test using a 5%level of significance. State the null and alternative hypotheses, find the p-value, state your conclusion, and identify the Type Iand Type IIerrors.

See all solutions

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