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Chapter 9: Q. 72 (page 542)

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22LTCC Intermediate Algebra students generated a mean of 7.24hours with a standard deviation of 1.93hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is X炉~

a.N7.24,1.9322

b.N(7.24,1.93)

c.t22

d.t21

Short Answer

Expert verified

We use a Studentt-distribution with n-1degrees of freedom i.e. X炉~t21.

Step by step solution

01

Student's t-distribution.

When we are testing a population means and when the population standard deviation is unknown we use a Student's t-distribution.

02

Using t21

Because in this test sample size is n=22, we use a Student's t-distribution with n-1degrees of freedom i.e.

X炉~t21

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Most popular questions from this chapter

"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.

If the alternative hypothesis has a not equals ( 鈮� ) symbol, you know to use which type of test?

"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!)

A normal distribution has a standard deviation of 1.We want to verify a claim that the mean is greater than12.

A sample of 36is taken with a sample mean of12.5.

H0:渭鈮�12

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Draw a graph that shows thep-value.

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5years. A study was then done to see if the meantime has increased in the new century. A random sample of 26first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3years with a standard deviation of 1.8years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

a.Ho_______
b.Ha_______
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