BurtsevD606Pres

Website registration.

A website is trying to increase registration for first-time visitors, exposing 1% of these visitors to a new site design. Of 752 randomly sampled visitors over a month who saw the new design, 64 registered.

1. Check any conditions required for constructing a confidence interval.

2. Compute the standard error.

3. Construct and interpret a 90% confidence interval for the fraction of first-time visitors of the site who would register under the new design (assuming stable behaviors by new visitors over time).

Create dataset and show summary

possible_entries <- c(rep("registered", 64), rep("not", 752 - 64))
summary(possible_entries)

##    Length     Class      Mode 
##       752 character character

Plot dataset

## [1] 64

## [1] 688

Conditions required for constructing a confidence interval.

The data must be sampled randomly and sample values must be independent. We meet this condition.

The data must be no more than 10% of the population. We meet this condition.

The sample size is considered suffciently large when np >= 10 and n(1 - p) >= 10.

n = 752 
p = 0.01
(n * p) >= 10

## [1] FALSE

(n * (1 - p)) >= 10

## [1] TRUE

Our sample is not suffciently large.

Compute the standard error.

se = sqrt((p * (1 - p) / n))
se

## [1] 0.003628346

Construct and interpret a 90% confidence interval

90% confidence interval is 1.65

yes_percent = yes_val * 100 / 752 # 8.510638
no_percent = no_val * 100 / 752
pe = yes_percent / 100 # 0.08510638

ci1 = pe - 1.65 * se 
ci2 = pe + 1.65 * se 
round(ci1 * 100, digits = 1)

## [1] 7.9

round(ci2 * 100, digits = 1)

## [1] 9.1

We are 90% confident that the actual proportion of first-time visitors of the site who would register under the new design is between 7.9% and 9.1%.