An archive of Mark's Fall 2017 Intro Stat course.

# Find a confidence interval for just a few random heights for 11:00 AM

mark

(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:

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.

brifro

T-Test of my Data:

View(df)
data.height

df$height [1] 70.04 62.41 58.34 60.06 65.26 68.59 64.04 60.72 62.76 69.36 63.17 67.40 height = c(62.41, 58.32, 60.06, 65.26, 68.59, 64.04, 60.72, 62.76, 69.36, 63.17, 67.40) t.test(height, conf.level = 0.95) One Sample t-test: data: height t = 59.657, df = 10, p-value = 4.255e-14 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 61.44249 66.21024 sample estimates: mean of x 63.82636 My 95% confidence interval according to my t-test is: approximately: [61.44249, 66.21024] shiller df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=shiller&length=12') df$height
[1] 66.51 64.74 66.20 70.88 62.36 67.63 65.84 66.72 65.87 61.69 69.80 69.69
t.test(df$height,conf.level = .95) One Sample t-test data: df$height
t = 82.442, df = 11, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
64.71894 68.26939
sample estimates:
mean of x
66.49417

My 95% confidence interval is [64.71894, 68.26939]

Megatog
df$height [1] 70.33 70.85 71.70 66.14 66.60 59.84 73.20 66.54 67.93 60.75 68.08 60.04 height = c(70.33, 70.85, 71.70, 66.14, 66.60, 59.84, 73.20, 66.54, 67.93, 60.75, 68.08, 60.04) t.test(height, conf.level = 0.95) One Sample t-test data: height t = 50.85, df = 11, p-value = 2.092e-14 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 63.94054 69.72612 sample estimates: mean of x 66.83333 According to my code, my 95% confidence interval is [63.94054, 69.72612]. emeli read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=mark&length=12') first_name last_name age gender height weight income 1 Donna Dinan 35 female 65.37 164.26 1947 2 Ramon Davis 20 male 66.59 139.53 22747 3 Mark Buss 23 male 74.58 124.21 15489 4 Lidia Elmore 52 female 63.87 153.64 8369 5 Nina Mcilhinney 40 female 61.33 118.81 3452 6 Phyllis Curtis 34 female 64.03 154.81 1149 7 Harold Lyons 52 male 70.98 199.52 10101 8 Francisco Lowe 36 male 68.09 171.67 122 9 Antonio Stockstill 40 male 67.65 137.28 14452 10 Esther Newkirk 42 female 60.96 153.37 3001 11 Walter Serna 44 male 68.11 220.62 2427 12 Donna Castro 36 female 63.38 106.92 15050 smoke100 exerany handedness 1 N Y R 2 Y Y R 3 N Y R 4 N Y R 5 N Y R 6 Y Y R 7 N Y R 8 N Y R 9 N N R 10 N Y R 11 Y N L 12 N Y R t.test(df$height)
One Sample t-test

data:  df$height t = 58.404, df = 11, p-value = 4.582e-15 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 63.02438 67.96062 sample estimates: mean of x 65.4925 Confidence interval [63.02438, 6796062] TaylorHinson df=read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=TaylorHinson&length=12') df$height
[1] 60.96 62.50 66.41 72.21 66.36 71.97 61.17 61.61 61.21 72.95 70.05 67.72

t.test(df$height) data: df$height
t = 48.68, df = 11, p-value = 3.372e-14
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.26418 69.25582
sample estimates:
mean of x
66.26

The 95% confidence Interval is [63.26418, 69.25582]

LunaLovegood

I used R to perform a t-test of my data.

# Out: 12 10
View(df)
df$height [1] 63.54 68.56 71.30 68.90 70.13 69.33 65.86 62.01 68.75 [10] 66.37 71.86 62.30 t.test(df$height, conf.level = 0.95)

One Sample t-test

data:  df$height t = 69.246, df = 11, p-value = 7.074e-16 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 65.26656 69.55177 sample estimates: mean of x 67.40917 As shown in the code, the 95% confidence interval is [65.26656, 69.55177] ceciliastack21 df height [1] 65.56 69.08 61.69 73.41 71.06 70.39 64.71 63.85 69.90 74.03 66.04 68.20 t.test(df height) One Sample t-test data: df$height
t = 61.361, df = 11, p-value = 2.666e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
65.71515 70.60485
sample estimates:
mean of x
68.16

My 95% Confidence interval is [65.71515, 70.60485]

TineriTalentati
bin/random_data.csv?

df$height [1] 65.29 65.92 68.00 65.71 63.13 64.97 66.01 [8] 71.29 69.46 74.12 70.51 67.37 d= c(65.29, 65.92, 68.00, 65.71, 63.13, 64.97, 66.01, 71.29, 69.46, 74.12, 70.51, 67.37) t.test(d, conf.level = 0.95) One Sample t-test data: d t = 74.309, df = 11, p-value = 3.26e-16 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 65.64465 69.65202 sample estimates: mean of x 67.64833 According to my t.test, my 95% confidence interval is [65.64465, 69.65202]. everyrose I start by pulling data using R, and focusing on the first 12 values in the height column. df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=everyrose&length=12') dim(df) [1] 12 10 df$height
[1] 66.20 68.34 67.91 64.24 69.57 71.67 70.24 66.91 58.83 65.63 62.01 70.84
height = c(66.20, 68.34, 67.91, 64.24, 69.57, 71.67, 70.24, 66.91, 58.83, 65.63, 62.01, 70.84)
t.test(height, conf.level=0.95)

T-Test Results:

One Sample t-test
data:  height
t = 61.145, df = 11, p-value = 2.771e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
64.45892 69.27275
sample estimates:
mean of x
66.86583

According to the T-Test, my 95% confidence interval is approximately [64.45892, 69.27275].

Elena
One Sample t-test
T-test of data
df$height [1] 69.93 71.61 62.95 63.55 70.88 67.97 70.67 65.66 69.36 65.09 61.87 71.22 data: df$height
t = 167.76, df = 99, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
66.253 67.839
sample estimates:
mean of x
67.046

my 95% confidence Interval according to my t-test is [66.253,67.839]
laurabeth
> df$height [1] 61.55 71.23 64.51 61.72 66.74 69.20 71.51 66.43 72.84 [10] 65.64 66.19 66.78 > height=c(61.55, 71.23, 64.51, 61.72, 66.74, 69.20, 71.51, 66.43, 72.84, 65.64, 66.19, 66.78) > t.test(height, conf.level = 0.95) One Sample t-test data: height t = 64.198, df = 11, p-value = 1.623e-15 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 64.73031 69.32636 sample estimates: mean of x: 67.02833 My 95% confidence interval is : [64.73031, 69.32636] oyang T-Test of my Data: df = read.csv('https://www.marksmath.org/cgi- bin/random_data.csv?username=oyang&length=12') df$height
[1] 62.62 65.00 70.25 64.87 64.42 64.11 64.87 68.33
[9] 64.65 63.77 63.58 64.70

One Sample t-test

t.test(df$height) data: df$height
t = 106.73, df = 11, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:  63.75505 66.43995
sample estimates:
mean of x
65.0975

My 95% confidence interval according to my t-test is approximately [63.75505, 66.43995]

emma0126

T-Test of my data:

View(df)
df$height [1] 71.83 67.39 69.44 65.96 62.63 60.08 69.15 61.98 68.77 70.16 63.60 67.72 height = c(67.39, 69.44, 65.96, 62.63, 60.08, 69.15, 61.98, 68.77, 70.16, 63.60, 67.72) t.test(height, conf.level = 0.95) One Sample t-test data: height t = 63.298, df = 10, p-value = 2.356e-14 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 63.75395 68.40605 sample estimates: mean of x 66.08 My 95% confidence level according to my t-test is approximately: [63.75395, 68.40605] vee First, copy and past that code, but make sure to change your username. > df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv? username=vee&length=12') > dim(df) [1] 12 10 df$height
[1] 71.61 66.86 71.35 68.63 67.97 67.77 68.43 69.55 70.41
[10] 65.43 74.05 67.72

Now run your t.test

> t.test(df$height, conf.level = 0.95) One Sample t-test data: df$height
t = 101.01, df = 11, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
67.64158 70.65509
sample estimates:
mean of x
69.14833

So, my confidence interval is, 67.64158 70.65509.

Nashman92

This is a T-Test of my data.
This is the data that was used.

df$height [1] 69.06 70.02 67.26 61.93 61.18 64.76 59.70 64.40 66.14 63.01 70.91 66.28 And here is the actual test and the results of the test. t.test(df$height, conf.level = 0.95)

One Sample t-test
data:  df$height t = 63.642, df = 11, p-value = 1.786e-15 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 63.12614 67.64886 sample estimates: mean of x 65.3875 My 95% confidence interval is [63.12614, 67.64886]. Chase df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=Chase&length=12') df$height
[1] 64.14 65.20 65.26 56.65 70.04 75.09 62.66 61.40 61.13 70.26 73.46 69.61

t.test(df$height) One Sample t-test data: df$height
t = 41.694, df = 11, p-value = 1.838e-13
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
62.74486 69.73847
sample estimates:
mean of x
66.24167

My 95% confidence interval is [62.74486, 69.73847]

Dancerlikens

df$height [1] 66.51 64.74 66.20 70.88 62.36 67.63 65.84 [8] 66.72 65.87 61.69 69.80 69.69 mean(df$height)

[1] 66.49417

One Sample t-test

data:  df$height t = -4.1328e-06, df = 11, p-value = 1 alternative hypothesis: true mean is not equal to 66.49417 95 percent confidence interval: 64.71894 68.26939 sample estimates: mean of x 66.49417 The 95% confidence interval for this data is: [64.71894, 68.26939] Erad df = read.csv('https://www.marksmath.org/cgi-bin/random_data.csv? username=Erad&length=12') df$height
[1] 62.07 65.59 63.22 63.23 64.87 65.75 73.80 62.51 69.93 68.49 63.51 69.42
df
first_name   last_name age gender height weight income smoke100 exerany handedness
1      Lashawn       Parks  39 female  62.07 177.27   6312        Y       Y          R
2        Clara     Landers  57 female  65.59 173.18   4364        N       N          R
3          Iva      Spears  32 female  63.22 171.55   4309        N       Y          R
4   Marguerite       Geise  57 female  63.23 173.17   4692        N       Y          R
5      Bernice      Willis  33 female  64.87 198.35  21841        N       N          L
6         Ruby      Miguel  38 female  65.75 206.60 240986        N       Y          R
7  Christopher      Duncan  44   male  73.80 127.45  53690        Y       Y          R
8        Amber        Geno  37 female  62.51 128.01   2252        N       N          R
9        Sammy Hertenstein  32   male  69.93 159.07     71        Y       Y          R
10       Devin       Mucci  36   male  68.49 148.74  90378        N       Y          R
11        June        Fuhr  23 female  63.51  84.43   8636        N       Y          R
12       Kevin     Rappold  25   male  69.42 213.33   2246        Y       Y          L
t.test(df$height) One Sample t-test data: df$height
t = 63.024, df = 11, p-value = 1.988e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.72645 68.33855
sample estimates:
mean of x
66.0325

My 95 percent confidence interval is (63.72645, 68.33855)

df$height [1] 72.02 63.39 59.91 68.15 61.87 73.16 66.37 67.97 65.46 [10] 65.13 74.63 63.32 t.test(df$height,conf.level = .95)

One Sample t-test

data:  df\$height
t = 50.321, df = 11, p-value = 2.345e-14
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
63.86073 69.70260
sample estimates:
mean of x
66.78167

My confidence level based is [63.86073,69.70260]