Question

A large cell phone provider reported that in 2010, 60% of its customers use phone only to make calls.   That same company has stated that customers using phone only to make calls has gone up. They surveyed 400 customers and found that only 230 of them are using phones mostly to make calls

1. Specify the null and alternative hypotheses.

1. H(0): p≥0.60 Versus H(a): p<0.60
2. H(0): p≤0.60 Versus H(a): p>0.60

2. The standard error (SE) of P0 is

1. 0.037
2. 0.058
3. 0.024
4. 0.047

3. The value of the test statistic is

1. -1.02
2. -0.52
3. -0.81
4. -3

4. The p-value is

1. 0.21
2. 0.16
3. 0.30
4. 0.08

5. At α=0.10 and using the p-value

1. We do not reject H0
2. We reject H(0) in favor of H(a)

6. In light of your conclusion from the PRECEDING question, what test error could happen?

1. Type I error
2. Type II error

Answer 1

a)

H0: p >= 0.60

Ha: p < 0.60

b)

Standard error = sqrt [ p ( 1 - p) / n ]

= sqrt [ 0.60 * ( 1 - 0.60) / 400 ]

= 0.024

c)

Sample proportion = 230 / 400 = 0.575

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]  

= ( 0.575 - 0.6) / sqrt [ 0.6 * 0.4 / 400 ]

= -1.02

d)

p-value = P(Z < z) =

= P(Z < -1.02)

= 0.16

e)

Since p-value > 0.10 significance level, fail to reject H0.

f)

Since We fail to reject null hypothesis,, Type 2 error could happen.