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This module provides an review on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

The next two questions refer to the following real study:

A recent survey of U.S. teenage pregnancy was answered by 720 girls, age 12 - 19. 6% of the girls surveyed said they have been pregnant. ( Parade Magazine ) We are interested in the true proportion of U.S. girls, age 12 - 19, who have been pregnant.

Find the 95% confidence interval for the true proportion of U.S. girls, age 12 - 19, who have been pregnant.

0 . 0424 , 0 . 0770 size 12{ left (0 "." "0424",0 "." "0770" right )} {}

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The report also stated that the results of the survey are accurate to within ± 3.7% at the 95% confidence level. Suppose that a new study is to be done. It is desired to be accurate to within 2% of the 95% confidence level. What is the minimum number that should be surveyed?

2401

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Given: X ~ Exp ( 1 3 ) . Sketch the graph that depicts: P x > 1 size 12{P left (X>1 right )} {} .

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The next four questions refer to the following information:

Suppose that the time that owners keep their cars (purchased new) is normally distributed with a mean of 7 years and a standard deviation of 2 years. We are interested in how long an individual keeps his car (purchased new). Our population is people who buy their cars new.

60% of individuals keep their cars at most how many years?

7.5

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Suppose that we randomly survey one person. Find the probability that person keeps his/her car less than 2.5 years.

0.0122

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If we are to pick individuals 10 at a time, find the distribution for the mean car length ownership.

N 7,0 . 63 size 12{N left (7,0 "." "63" right )} {}

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If we are to pick 10 individuals, find the probability that the sum of their ownership time is more than 55 years.

0.9911

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For which distribution is the median not equal to the mean?

  • Uniform
  • Exponential
  • Normal
  • Student-t

B

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Compare the standard normal distribution to the student-t distribution, centered at 0. Explain which of the following are true and which are false.

  • As the number surveyed increases, the area to the left of -1 for the student-t distribution approaches the area for the standard normal distribution.
  • As the degrees of freedom decrease, the graph of the student-t distribution looks more like the graph of the standard normal distribution.
  • If the number surveyed is 15, the normal distribution should never be used.
  • True
  • False
  • False
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The next five questions refer to the following information:

We are interested in the checking account balance of a twenty-year-old college student. We randomly survey 16 twenty-year-old college students. We obtain a sample mean of $640 and a sample standard deviation of $150. Let X size 12{X} {} = checking account balance of an individual twenty year old college student.

Explain why we cannot determine the distribution of X size 12{X} {} .

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If you were to create a confidence interval or perform a hypothesis test for the population mean checking account balance of 20-year old college students, what distribution would you use?

student-t with df = 15 size 12{ ital "df"="15"} {}

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Find the 95% confidence interval for the true mean checking account balance of a twenty-year-old college student.

560 . 07 , 719 . 93 size 12{ left ("560" "." "07","719" "." "93" right )} {}

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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