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Chapter 9: Q.5 (page 536)

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the proportion is actually less. What is the random variable? Describe in words.

Short Answer

Expert verified

The proportion of people picked randomly at Times square in new york city is the random variable.

Step by step solution

01

introduction

A random variable is a numerical formalization of an amount or article which relies upon random occasions.

02

explanation

The probability that a person picked at random in Times Square in New York City is visiting the area is 0.83

Hence we can conclude that the proportion of people picked randomly at Times square in new york city is the random variable

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Most popular questions from this chapter

"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!)

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

a. Is this a test of one mean or proportion?

b. State the null and alternative hypotheses.

H0:

Ha:

c. Is this a right-tailed, left-tailed, or two-tailed test?

d. What symbol represents the random variable for this test?

e. In words, define the random variable for this test.

f. Calculate the following:

i.x=

ii.role="math" localid="1649760873126" n=

iii.p'=

g. Calculate role="math" localid="1649760901479" 蟽x=Show the formula set-up.

h. State the distribution to use for the hypothesis test.

i. Find the p-value.

j. At a pre-conceived 伪=0.05, what is your:

i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):

Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys361 schoolmates and finds that135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

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 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use 伪 = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

"Untitled," by Stephen Chen

I've often wondered how software is released and sold to the public. Ironically, I work for a company that sells products with known problems. Unfortunately, most of the problems are difficult to create, which makes them difficult to fix. I usually use the test program X, which tests the product, to try to create a specific problem. When the test program is run to make an error occur, the likelihood of generating an error is1%.

So, armed with this knowledge, I wrote a new test program Y that will generate the same error that test programX creates, but more often. To find out if my test program is better than the original, so that I can convince the management that I'm right, I ran my test program to find out how often I can generate the same error. When I ran my test program50 times, I generated the error twice. While this may not seem much better, I think that I can convince the management to use my test program instead of the original test program. Am I right?
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