Find a confidence interval for just a few random heights for 8:00 AM

(5 pts)

By now, we’ve played with random data quite a few times. We’re going to do so again but, this time, we’re not going to import quite so much data - only 12 rows. I can do this like so:

df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=mark&length=12')
dim(d)

# Out: 12 10

That output indicates that I’ve got only twelve rows of data.

Your assignment: Perform a t.test on the column of heights and report your confidence interval. As always, your code should be typeset as code and your answer should be typeset as prose.

The t-test of my data looks like this:
One Sample t-test

data:  df$height
t = 62.604, df = 11, p-value = 2.139e-15
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
63.87329 70.54171
sample estimates:
mean of x 
67.2075 

*** My Confidence Intervals at a 99% level are: approximately: 63.87 and 70.54

The t-test looks like this:

One Sample t-test

data:  df$height
t = 50.229, df = 11, p-value = 2.393e-14
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
64.26174 70.15160
sample estimates: mean of x 
67.20667 

This means my confidence interval would be 64.26174, and 70.15160.

df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=blaiser1&length=12')
df
df$height
height = c(66.22, 59.85, 56.30, 65.49, 66.14, 60.76, 58.63, 66.80, 66.69, 63.90, 67.78, 56.99)
t.test(height, conf.level=0.99)
	One Sample t-test

data:  df$height
t = 52.047, df = 11, p-value = 1.621e-14
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
59.20533 66.71967
sample estimates:
mean of x 
62.9625 

i added commas just in case.

please be right.PNG833x597 22.6 KB

heights:
61.52
63.27
72.41
69.35
62.22
63.10
69.23
63.64
65.02
67.10
65.00
64.90

df height [1] 61.52 63.27 72.41 69.35 62.22 63.10 69.23 63.64 65.02 67.10 65.00 64.90 t.test(df height)

data: df$height

t = 68.584, df = 11, p-value = 7.86e-16

alternative hypothesis: true mean is not equal to 0

95 percent confidence interval:
63.45930 67.66737

sample estimates:

mean of x
65.56333

t.test(df$height,conf.level = .95)

	One Sample t-test

data:  df$height
t = 58.416, df = 11, p-value = 4.572e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 63.06581 68.00419
sample estimates:
mean of x 
   65.535 

To a 95% confidence interval my true mean is between 63.06581 and 68.00419.

df$height
[1] 68.33 62.78 64.10 62.61 69.29 70.42 67.01 70.71 69.30 63.37 71.98 61.74
t.test(df$height)

One Sample t-test

data:  df$height
t = 62.997, df = 11, p-value = 1.997e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
64.46935 69.13732
sample estimates:
mean of x 
66.80333 

We are 99% confident that our number falls in-between the heights 64.47 and 69.14

(df$height)

One Sample t-test

data:  df$height
t = 49.541, df = 11, p-value = 2.783e-14
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
62.64496 68.47004
sample estimates:
mean of x 
65.5575 

We are 99% confident that our number falls in between the heights of 62.64 and 68.47.

This is the t-test

t.test(df$height,conf.level=.95)

One Sample t-test

data:  df$height
t = 53.988, df = 11, p-value = 1.085e-14
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 64.64025 70.13475
sample estimates:
mean of x 
  67.3875

df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=jackvines1&length=12')
height = df$height

In the above code I have read in my list of data and set the variable height to the list of 12 heights in my data.

t.test(height)

One Sample t-test

data:  height
t = 58.249, df = 11, p-value = 4.718e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.77956 68.78878
sample estimates:
mean of x 
66.28417 

My 95% confidence interval according to my t.test output is: [63.77956, 68.78878]

T-Test of my Data:

df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=ncarsloan&length=12')
t.test(df$height, conf.level = .95)

One Sample t-test

data:  df$height
t = 67.593, df = 11, p-value = 9.222e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
64.61839 68.96828
sample estimates:
mean of x 
66.79333 

This means my confidence interval would be 64.61839 and 68.96828

df$height
[1] 65.37 66.59 74.58 63.87 61.33 64.03 70.98 68.09 67.65 60.96 68.11 63.38

One Sample t-test

data: df$height
t = 57.953, df = 11, p-value = 4.989e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.72909 68.76091
sample estimates:
mean of x
66.245

df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=asiarenee5&length=12')

> df$height
 [1] 61.31 70.63 66.22 67.50 61.29 64.65 62.35 67.51 68.22 62.39 70.42 65.20
> t.test(df$height,conf.level=0.99)

    One Sample t-test

 data:  df$height
 t = 68.298, df = 11, p-value = 8.23e-16
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
62.65585 68.62582
sample estimates:
mean of x 
65.64083 

I am 99% confident that my number falls in between 62.66 and 68.63

df = read.csv(‘https://www.marksmath.org/cgi-bin/random_data.csv?username=avavball13&length=12’)
df
df$height
[1] 64.93 68.30 68.90 70.14 63.42 61.01 64.30 71.53 64.76 69.91 69.97 61.39
t.test(height, conf.level=0.99)
One Sample t-test

data: df$height
t = 52.047, df = 11, p-value = 2.621e-14
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
61.20533 67.71967
sample estimates:
mean of x
64.9625

t.test data:

df = read.csv('https://www.marksmath.org/cgi_bin/random_data.csv?username=alogan3&length=12')

One Sample t-test

data:  height
t = 43.343, df = 11, p-value = 1.202e-13
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.02503 69.76830
sample estimates:
mean of x 
66.39667 

Based off of my t.test date, my 95% confidence interval is (63.02503, 69.76830)

df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=amandanail&length=12')

One Sample t-test

data:  df$height
t = 55.121, df = 11, p-value = 8.641e-15
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
62.91899 70.43267
sample estimates:
mean of x 
66.67583

I am 99% confident that my number falls between 62.91 and 70.43

t.test(df$height,conf.level = .95)

One Sample t-test

data: df$height
t = 58.416, df = 11, p-value = 4.572e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.06581 68.00419
sample estimates:
mean of x
65.535
To a 95% confidence interval my true mean is between 63.06581 and 68.00419.