Learning Check 8.1

The chief difference is replacement. Bootstrapping is a replacement method, and sampling distribution is a randomization method.

Learning Check 8.2

The bootstap distribution lies more because of the fact it replaces values.

Learning Check 8.3

When the percentile method is true. And have a 95% confidence.

Learning Check 8.4

The mean will not be as accurate. One will need to do many tests to find a valid answer.

Learning Check 8.5

# A tibble: 1 x 2
  `2.5%` `97.5%`
   <dbl>   <dbl>
1     NA      NA
# A tibble: 1 x 1
   stat
  <dbl>
1 1996.

1.

# A tibble: 1 x 1
    mean
   <dbl>
1 51049.

2.

# A tibble: 1,000 x 19
# Groups:   replicate [1]
   replicate state emp_length  term homeownership annual_income
       <int> <chr>      <dbl> <dbl> <chr>                 <dbl>
 1         1 FL            NA    36 mortgage              94000
 2         1 CT             0    36 mortgage              52000
 3         1 OH            NA    60 mortgage              70000
 4         1 NY            10    36 mortgage              90000
 5         1 MI            10    60 mortgage              60000
 6         1 NY             1    36 mortgage              52000
 7         1 CT            10    36 mortgage             114000
 8         1 TX            10    36 mortgage              48000
 9         1 OK             8    60 rent                  30000
10         1 MO             2    60 rent                  47000
# ... with 990 more rows, and 13 more variables: verified_income <chr>,
#   debt_to_income <dbl>, total_credit_limit <dbl>,
#   total_credit_utilized <dbl>, num_cc_carrying_balance <dbl>,
#   loan_purpose <chr>, loan_amount <dbl>, grade <chr>,
#   interest_rate <dbl>, public_record_bankrupt <dbl>, loan_status <chr>,
#   has_second_income <lgl>, total_income <dbl>

3.

Setting `type = "bootstrap"` in `generate()`.
# A tibble: 1,000 x 2
   replicate   stat
       <int>  <dbl>
 1         1 52092.
 2         2 51876.
 3         3 53927.
 4         4 52285.
 5         5 50170.
 6         6 50506.
 7         7 51699.
 8         8 50902.
 9         9 52123.
10        10 51284.
# ... with 990 more rows
2.
# A tibble: 1 x 1
    mean
   <dbl>
1 51414.
3.
# A tibble: 1 x 2
  `2.5%` `97.5%`
   <dbl>   <dbl>
1 48694.  54275.
4.
# A tibble: 1 x 2
   lower  upper
   <dbl>  <dbl>
1 46791. 52401.
5.