Answered: The following is a random sample of IQ…

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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Practice Quiz 8
The following is a random sample of IQ scores from a prestigious college:
94 101 109 109 115 117 119 125 125 125 134 146 155

1) Find the mean, median, mode, and standard deviation of the data.

2) Use your answers from problem 1 to find a 98% confidence interval for the true mean IQ of
the population.

3) If we want to the margin of error for the preceding interval to be less than 5 IQ points, how
many total students must be sampled?

4) A “superior” IQ is defined as being 120 or higher. How many students in our sample does this
apply to? Use this to find the proportion of students with a superior IQ and construct a 90%
confidence interval for the true proportion of students with superior IQ at this school.

5) If we want to the margin of error for the preceding interval to be less than 10 percentage
points, how many total students must be sampled?

6) The IQ test is designed to have a mean of 100. Does that value fall into the confidence
interval from problem 2? Does this suggest that the average IQ of students at this prestigious
college are higher than the general population?

this is the answer key

Quiz 8:
1) Mean: 121.08, Median: 119, Mode: 125, St. Dev.:17.01
2) μ∈(108.43,133.72)
3) n≥63
4) X=6, ?̂ =.1643, ? ∈(.2341,.689)
5) n≥68
6) Since 100 is not contained in the confidence interval, we
can be 98% confident that the average IQ of students at
this prestigious college is higher than the general
population.

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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