Chapters 18-19 Summative Assessment

Question

The manager of an chicken farm expects about 70% of his chickens to grow large enough to be considered for consumption. At least how many chickens must he sample to be 90% confident of estimating the true proportion within ± 4%?

a	19
b	89
c	356
d	23
e	505

Question 3 

An ice cream shop owner wants to see if more than 80% of customers enjoy a new flavor. She takes a random sample of customers who tried the flavor at the unveiling event and asks, in an anonymous survey, if the customers enjoyed the flavor. Which set of hypotheses should she test? 

a	H0 : p < 0.80	HA: p ≠ 0.80
b	H0 : p = 0.80	HA: p > 0.80
c	H0 : p = 0.80	HA: p < 0.80
d	H0 : p < 0.80	HA: p > 0.80
e	H0 : p > 0.80	HA: p = 0.80

Answer 1

sample size for proportion (n) = p*(1-p)(z-critical/E)^2

where p is proportion, z-critical is z-score for confidence level and E is +/- margin of error

p = 0.7, z-critical for 90% is 1.645 and E is given as 0.04 (4% in decimal), so

n = 0.7*0.3*(1.645/0.04)^2 = 355.16 ----> 356 (c)

Question 3

Ho: p = 0.8

Ha: p > 0.8 (b)