Problem I

A

This is the mean of student height:

## [1] 68.10265

This is the standard deviation of height:

## [1] 4.13815

B

This is the proportion of observations within 2 standard deviations of the mean:

0.9722222

This suggests student heights are normally distributed because it is very close to a 98% proportion.

C

This is a QQ plot for height

D

## [1] 67.89634
## [1] 68.30895

The 95% confidence interval for average student height is 67.8963, 68.309

Problem II

A

The student pulse mean is 74.2162791

The student pulse standard deviation is 18.2218379

B

The proportion of observations within 1 standard deviations is 0.8010336. This suggests the data is not normally distributed because the proportion does not match the empirical rule.

C

D

This is the 99% confidence interval for average student pulse:

## [1] 73.02185
## [1] 75.41071

Problem III

A

B

The 90% confidence interval for average student GPA is

## [1] 3.617058
## [1] 3.645042

C

The interval for C means that we are 90% confident that the true average highschool student GPA is between 3.6170576, 3.6450424.

D

We did need not need to assume the data was normally distributed to be valid because the sample size is over 30 and fits the central limit theorem.

Appendix

{r, echo=FALSE}

student <- read.csv(“C:/Users/Jerry/Desktop/student.csv”)

mean(student$height)

sd(student$height)

the.mean = mean(student$height)

the.sd = sd(student$height)

lower.bound = the.mean - 1:3*the.sd

upper.bound = the.mean + 1:3*the.sd

two.sd = mean(student\(height > lower.bound[2] & student\)height < upper.bound[2])

r two.sd

qqnorm(student$height,main = “Normal Probability Plot for Student Height”)

qqline(student$height)

the.stuff = t.test(student$height, conf.level = 0.95)

the.stuff$conf.int[1]

the.stuff$conf.int[2]

my.CI = round(the.stuff$conf.int,digits = 4)

r my.CI[1] r my.CI[2]

themean = mean(student$pulse)

thesd = sd(student$pulse)

lower.bound = themean - 1:3*thesd

upper.bound = themean + 1:3*thesd

one.sd = mean(student\(pulse > lower.bound[1] & student\)pulse < upper.bound[1])

qqnorm(student$pulse,main = “Normal Probability Plot for Student pulse”)

qqline(student$pulse)

thestuff = t.test(student$pulse, conf.level = 0.99)

thestuff$conf.int[1]

thestuff$conf.int[2]

my.CI = round(the.stuff$conf.int,digits = 4)

hist(student$hsGPA, main = “Histogram of Highschool Student GPA”, xlab = “Student Highschool GPA”)

stuff = t.test(student$hsGPA, conf.level = 0.90)

stuff$conf.int[1]

stuff$conf.int[2]

my.CI = round(thestuff$conf.int,digits = 4)