Download Lab1KEY

Lab Assignment 1 (Due: 4/14/17)
1. (Z-tests for a population mean and confidence interval) In Example 11.1 we saw that the
distribution of heights of young women aged 18 to 24 is approximately Normal with mean µ =
64.5 inches and standard deviation σ = 2.5 inches. A random sample of 93 female undergraduate
students at the University of California at Irvine produced a sample mean height of 62.7 inches.
Is there evidence that the mean height of all female undergraduate students at UC-Irvine is
different from the mean height of all young women in the United States? Use the level of
significance α = 0.05. Try both confidence interval and p-value approaches. Interpret your
results. Hint: > install.packages("TeachingDemos")
> library(TeachingDemos)
Download ta14-01.xls and then use the z.test.
Downloading ta14-01.xls file: Save ta14-01.xls file as ta14-01.csv file on your desktop.
Then type the following:
> ta14.01 = read.csv(file=file.choose(),header=TRUE,sep=",")
This will ask you to choose a file that you wish to download. Double click ta14-01.csv
> z.test(ta14.01$Height,mu=64.5,sd=2.5,conf.level=.95)
One Sample z-test
data: ta14.01$Height
z = -6.9891, n = 93.00000, Std. Dev. = 2.50000, Std. Dev. of the sample
mean = 0.25924, p-value = 2.767e-12
alternative hypothesis: true mean is not equal to 64.5
95 percent confidence interval:
62.18008 63.19627
sample estimates:
mean of ta14.01$Height
62.68817
Interpretation:
Confidence interval approach: Since the 95% confidence interval, (62.18, 63.20), does
not include 64.5, there is a statistically significant evidence at 5% level of significance
that the mean height of all female undergraduate students at UC-Irvine is different than
that of all young women in the United States.
P-value approach: Since the p-value = 2.767e-12 is less than α = 0.05, we conclude that
there is a statistically significant evidence at 5% level of significance that the mean height
of all female undergraduate students at UC-Irvine is different from the mean height of all
young women in the United States.