5.20 High School and Beyond, Part I: The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below.(d) What type of error might we have made? Explain what the error means in the context of the application.( )Type I( )Throwing Error( )Type II( )Fielding Error(e) Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning.( )yes, because the evidence was not strong enough to suggest that average reading and writing scores differ( )no, because most people will not earn an average score of 0 on either exam( )yes, because there is almost a 0% chance that average reading and writing scores are the same( ) no, because we rejected the idea that average reading and writing scores are equal 5.20 High School and Beyond, Part I: The National Center of Education Statistics conducted a survey ofhigh school seniors, collecting test data on reading, writing, and several other subjects. Here we examine asimple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scoresas well as a histogram of the differences in scores are shown below.8060-4020readwrite40 –3020-10-20-101020Differences in scores (read– write)Scores

Answered: .20 High School and Beyond, Part I:…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5.20 High School and Beyond, Part I: The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below.

(d) What type of error might we have made? Explain what the error means in the context of the application.

( )Type I
( )Throwing Error
( )Type II
( )Fielding Error

(e) Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning.

( )yes, because the evidence was not strong enough to suggest that average reading and writing scores differ
( )no, because most people will not earn an average score of 0 on either exam
( )yes, because there is almost a 0% chance that average reading and writing scores are the same
( ) no, because we rejected the idea that average reading and writing scores are equal

5.20 High School and Beyond, Part I: The National Center of Education Statistics conducted a survey of
high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a
simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores
as well as a histogram of the differences in scores are shown below.
80
60-
40
20
read
write
40 –
30
20-
10
-20
-10
10
20
Differences in scores (read– write)
Scores

Expert Solution

Step 1

(d) What type of error might we have made? Explain what the error means in the context of the application.

Null Hypothesis $H_{0} : μ_{r e a d i n g} - μ_{w r i t i n g} = 0$ i.e., there is no significant difference between the average reading and writing scores.

Alternative Hypothesis $H_{1} : μ_{r e a d i n g} - μ_{w r i t i n g} \neq 0$ i.e., there is a significant difference between the average reading and writing scores.

Type 1 error : Rejecting $H_{0}$ when it is true.

Type 2 error : Accepting $H_{0}$ when it is false

Since, we failed to reject (accept) $H_{0}$ (previous part) and there could be a chance that it was actually false, then the error that might occur is Type 2 error.

If we took larger samples, we would decrease our chances of making a type 2 error.

Correct option : Type 2 error

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