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Tan Melissa Frappy 7 - AP stats chapter 7

AP stats chapter 7
Course

Statistics for Social Sciences (STAT221)

9 Documents
Students shared 9 documents in this course
Academic year: 2020/2021
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University of Washington

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Chapter 7 FRAPPY!

Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

The principal of a large high school is concerned about the number of absences for students at his school. To investigate, he prints a list showing the number of absences during the last month for each of the 2500 students at the school. For this population of students, the distribution of absences last month is

skewed to the right with a mean of = 1 and a standard deviation of 1.

Suppose that a random sample of 50 students is selected from the list printed by the principal and the sample mean number of absences is calculated.

(a) What is the shape of the sampling distribution of the sample mean? Explain.

(b) What are the mean and standard deviation of the sampling distribution of the sample mean?

(c) What is the probability that the mean number of absences in a random sample of 50 students is less than 1?

(d) Because the population distribution is skewed, the principal is considering using the median number of absences last month instead of the mean number of absences to summarize the distribution. Describe how the principal could use a simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50.

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Tan Melissa Frappy 7 - AP stats chapter 7

Course: Statistics for Social Sciences (STAT221)

9 Documents
Students shared 9 documents in this course

University: University of Washington

Was this document helpful?
Chapter 7 FRAPPY!
Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the
correctness of your methods as well as on the accuracy and completeness of your results and
explanations.
The principal of a large high school is concerned about the number of absences for students at his
school. To investigate, he prints a list showing the number of absences during the last month for each of
the 2500 students at the school. For this population of students, the distribution of absences last month is
skewed to the right with a mean of
= 1.1 and a standard deviation of
1.4.
Suppose that a random sample of 50 students is selected from the list printed by the principal and the
sample mean number of absences is calculated.
(a) What is the shape of the sampling distribution of the sample mean? Explain.
(b) What are the mean and standard deviation of the sampling distribution of the sample mean?
(c) What is the probability that the mean number of absences in a random sample of 50 students is less
than 1?
(d) Because the population distribution is skewed, the principal is considering using the median number
of absences last month instead of the mean number of absences to summarize the distribution. Describe
how the principal could use a simulation to estimate the standard deviation of the sampling distribution of
the sample median for random samples of size 50.
The shape of the sampling distribution of the sample mean would be
approximately normal distributed because the sample of n=50 is > than 30
(50>=30)
= 1.1 (absences)
= 1.4
50
= 0.198 (absences)
P( x <1)= normalcdf (lower: -1000, upper: 1, sd: 0.198 )
there is about a 30.68% probability that the mean number of absences in a
random sample of 50 students is less than 1
to start off, the principal could take many, many samples of 50 students and Þnd
the median for each of the sample sets. After that, the principal could calculate the
standard deviation of the sampling distribution from the sample medians

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