NUR 5201
Review of Week 5
Re-cap:
When finding a CI, we are estimating the
value of a ________________
Which ____________ you are estimating,
determines which formula you should use.
A (1 – α)% Confidence Interval for p:
Key Word: Estimate with (1 – α)% confidence the proportion…..
𝑝Ƹ ∙ 𝑞ො
𝑝Ƹ ± 𝑍𝛼ൗ ∙
2
𝑛
𝑁(0, 1)
𝛼ൗ
2
1-α
z
Assuming n∙𝑝Ƹ ≥ 5 and n∙𝑞ො ≥ 5
95
A (1 – α)% Confidence Interval for μ
Key Word: Estimate with (1 – α)% confidence the average (or mean)…..
𝑥ҧ ± 𝑡
𝛼Τ
2
𝑡(𝑛−1)
1-α
𝑠
∙
𝑛
𝛼ൗ
2
t
Assuming the population is normally distributed
(use QQ-plot to verify)
t stands for the
student’s t-distribution
with degrees of
freedom, df = n – 1
(pg 339)
Notice the Similarities
𝑝Ƹ ± 𝑍𝛼ൗ ∙
2
𝑥ҧ ± 𝑡
𝑝Ƹ ∙ 𝑞ො
𝑛
𝛼Τ
2
N(0,1)
𝑡(𝑛−1)
𝛼ൗ
2
1-α
z
t
𝑠
∙
𝑛
Determining n when estimating p
sample
size
𝑍2
𝑛 = 2 𝑝Ƹ ∙ 𝑞ො
𝐸
Margin of Error
(The amount “within”)
Based on
the level of
confidence
Known from a
previous
example
Or assume both
equal 1/2
Recall we always round up when finding n
Know your KEY words!!
Estimate with ___% confidence….
________________________________
The average/mean
________________________________
The proportion/%
What sample size is needed to ….
________________________________
________________________________
Example 1: The city manager would like to estimate the average rent the
tenants in his town pay. A random sample of 40 renters was obtained and
the average rent for them was $1250 per month with standard deviation
$125. Estimate with 99% confidence the average rent per month the
tenants in his town pay.
The city mayor would like to estimate the proportion of renters that
pay over $2000 per month for rent. The mayor would like the
estimate to be within 3% with 99% confidence. What sample size
should the city mayor use?