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library(openintro)

## Warning: package 'openintro' was built under R version 4.2.3

## Loading required package: airports

## Warning: package 'airports' was built under R version 4.2.3

## Loading required package: cherryblossom

## Warning: package 'cherryblossom' was built under R version 4.2.3

## Loading required package: usdata

## Warning: package 'usdata' was built under R version 4.2.3

yrbss

## # A tibble: 13,583 × 13
##      age gender grade hispanic race        height weight helme…¹ text_…² physi…³
##    <int> <chr>  <chr> <chr>    <chr>        <dbl>  <dbl> <chr>   <chr>     <int>
##  1    14 female 9     not      Black or A…  NA      NA   never   0             4
##  2    14 female 9     not      Black or A…  NA      NA   never   <NA>          2
##  3    15 female 9     hispanic Native Haw…   1.73   84.4 never   30            7
##  4    15 female 9     not      Black or A…   1.6    55.8 never   0             0
##  5    15 female 9     not      Black or A…   1.5    46.7 did no… did no…       2
##  6    15 female 9     not      Black or A…   1.57   67.1 did no… did no…       1
##  7    15 female 9     not      Black or A…   1.65  132.  did no… <NA>          4
##  8    14 male   9     not      Black or A…   1.88   71.2 never   <NA>          4
##  9    15 male   9     not      Black or A…   1.75   63.5 never   <NA>          5
## 10    15 male   10    not      Black or A…   1.37   97.1 did no… <NA>          0
## # … with 13,573 more rows, 3 more variables: hours_tv_per_school_day <chr>,
## #   strength_training_7d <int>, school_night_hours_sleep <chr>, and abbreviated
## #   variable names ¹​helmet_12m, ²​text_while_driving_30d, ³​physically_active_7d

yrbss_samp

## # A tibble: 100 × 13
##      age gender grade hispanic race        height weight helme…¹ text_…² physi…³
##  * <int> <chr>  <chr> <chr>    <chr>        <dbl>  <dbl> <chr>   <chr>     <dbl>
##  1    16 female 11    not      Black or A…   1.5    52.6 never   1-2           0
##  2    17 male   11    not      White         1.78   74.8 rarely  0             7
##  3    17 male   11    not      White         1.75  107.  never   0             7
##  4    15 male   10    hispanic <NA>          1.68   66.7 never   did no…       3
##  5    18 male   12    not      Black or A…   1.7    80.3 never   did no…       0
##  6    15 female 9     not      Black or A…   1.57   46.3 <NA>    did no…       4
##  7    16 male   10    not      White         1.78   81.6 always  0             7
##  8    16 male   10    not      Black or A…   1.63   56.7 never   0             5
##  9    14 male   9     hispanic White         1.63   54.4 never   0             7
## 10    17 male   11    not      Black or A…   1.83   92.5 never   did no…       6
## # … with 90 more rows, 3 more variables: hours_tv_per_school_day <chr>,
## #   strength_training_7d <dbl>, school_night_hours_sleep <chr>, and abbreviated
## #   variable names ¹​helmet_12m, ²​text_while_driving_30d, ³​physically_active_7d

set.seed(0)
n = 1000
sample_means = rep(NA,n )
for(i in 1:n){
  sample_means[i] = mean(rnorm(100, mean=3.75, sd= 2.556))
}
head(sample_means)

## [1] 3.807941 3.633570 3.921818 3.758244 3.625871 3.529897

hist(sample_means, main = "", xlab = "Sample mean", ylab = "Frequency", col = "steelblue")

mean(sample_means)

## [1] 3.753603

sd(sample_means)

## [1] 0.255857