Stat 411/511

Homework 1

Due on canvas Oct 9th

#1 Central Limit Theorem

Do Problems 4.35 & 4.36 from OpenIntro.

If you want more review read Sections 4.1, 4.2 & 4.4 in OpenIntro

You might also want to play with this demonstration:

#2 Displaying and describing distributions

Examine the plots in q2-hists.pdf. Each row is a different sample dataset, each column is a different type of plot you might use to examine the distribution of a sample.

a) For each sample, describe the shape of its distribution in one sentence.

b) Discuss the advantages and disadvantages of each type of plot. What factors influence which plot is most appropriate?

#3 t-based CI

Researchers collected a simple random sample of 36 children who had been identified as gifted in a large city. The IQ of their mother and father is provided (along with some other measurements) in the gifted dataset.

(This is based on a question from the OpenIntro stats book ( and is released under a Creative Commons BY-NC-SA 3.0 license.)

You can load the data and add a column to the gifted data for the differences in the IQ of the children’s mother and father using this code:

gifted$diff <- gifted$fatheriq - gifted$motheriq

A. Using R, construct a 95% t-based confidence interval for the mean difference in IQ between the mother’s and father’s IQ score.

B. Write a one sentence summary of the interval in the context of the data.