Question

The number of successes and the sample size for a simple random sample from a population are given below.

xequals=3535​,

nequals=5050​,

Upper H 0H0​:

pequals=0.60.6​,

Upper H Subscript aHa​:

pgreater than>0.60.6​,

alphaαequals=0.050.05

a. Determine the sample proportion.

b. Decide whether using the​ one-proportion z-test is appropriate.

c. If​ appropriate, use the​ one-proportion z-test to perform the specified hypothesis test.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.60

Ha : p > 0.60

n = 50

x = 35

a ) = x / n = 35 / 50 =0.70

P0 = 0.60

1 - P0 = 1 - 0.60 = 0.40

b ) Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.70 - 0.60 / [0.60 *0.40 / 50 ]

= 1.44

Test statistic = z =1.44

P(z > 1.44 ) = 1 - P(z < 1.44 ) = 1 - 0.9251

c ) P-value = 0.0749

= 0.05

P-value >

0.0749 > 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that