Question

Consider the following hypotheses:

H₀: p ≥ 0.48

H_A: p < 0.48

Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

		p-value
a.	x = 50; n = 122
b.	x = 118; n = 329
c.	p¯p¯ = 0.42; n = 41
d.	p¯p¯ = 0.42; n = 413

Answer 1

a)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4098 - 0.48)/sqrt(0.48*(1-0.48)/122)
z = -1.55

P-value Approach
P-value = 0.0606

b)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3587 - 0.48)/sqrt(0.48*(1-0.48)/329)
z = -4.4

P-value Approach
P-value = 0

.

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.42 - 0.48)/sqrt(0.48*(1-0.48)/41)
z = -0.77

P-value Approach
P-value = 0.2206

d)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.42 - 0.48)/sqrt(0.48*(1-0.48)/413)
z = -2.44

P-value Approach
P-value = 0.0073