Question

Make sure you answer these questions using the normal table on page #5 of your formula packet. Do NOT use a calculator or other means of determining normal curve areas.

(a) Find the p - value for the test statistic ?=1.64z=1.64 for the following null and alternative hypotheses: the chart has a proportion of .95 and a percentile of 95
?0:?=50H0:μ=50
??:?>50HA:μ>50
The p - value is

(b) Find the p - value for the test statistic ?=1.75z=1.75 for the following null and alternative hypotheses: the chart has a proportion of .96 and a percentile of 96
?0:?=50H0:μ=50
??:?≠50HA:μ≠50
The p - value is

Answer 1

Solution :

a) This is the right tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 50

H_a : > 50

Test statistic = z = 1.64

P(z > 1.64) = 1 - P(z < 1.64) = 1 - 0.9495

P-value = 0.0505

b) This is the two tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 50

H_a :    50

Test statistic = z = 1.75

P(z > 1.75) = 1 - P(z < 1.75) = 1 - 0.9599 = 0.0401

P-value = 2 * P(z > 1.75)

P-value = 2 * 0.0401

P-value = 0.0802