Question

A poll of

2,142

randomly selected adults showed that

92​%

of them own cell phones. The technology display below results from a test of the claim that

91​%

of adults own cell phones. Use the normal distribution as an approximation to the binomial​ distribution, and assume a

0.05

significance level to complete parts​ (a) through​ (e).

Test of p=0.91 vs p≠0.91
Sample	X	N	Sample p	​95% CI	​Z-Value	​P-Value
1	1970	2,142	0.919701	​(0.908193​,0.931210​)	1.57	0.117

a. Is the test​ two-tailed, left-tailed, or​ right-tailed?

​Left-tailed test

Right tailed test

​Two-tailed test

b. What is the test​ statistic?

The test statistic is

nothing.

​(Round to two decimal places as​ needed.)

c. What is the​ P-value?

The​ P-value is

nothing.

​(Round to three decimal places as​ needed.)

d. What is the null hypothesis and what do you conclude about​ it?

Identify the null hypothesis.

A.

H0: p≠0.91

B.

H0: p>0.91

C.

H0: p<0.91

D.

H0: p=0.91

Choose the correct answer below.

A.

Fail to reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

α.

B.

Reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

α.

C.

Fail to reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

α.

D.

Reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

α.

e. What is the final​ conclusion?

A.There

is not

sufficient evidence to support the claim that

91​%

of adults own a cell phone.

B.There

is not

sufficient evidence to warrant rejection of the claim that

91​%

of adults own a cell phone.

C.There

is

sufficient evidence to support the claim that

91​%

of adults own a cell phone.

Answer 1

Using the result given the answers are a) Two tailed test b) Test statistic z=1.57 c) P-value 2*P(21.57) = 0.117 or 0.1164 d) Null hypothesis Ho: p=0.91 Option D is correct Fail to reject the null hypothesis since p-value > 0 Option A is correct e) Final conclusion There is not sufficient evidence to warrant the rejection of the claim that 91% of adults own a cell phone Option B is correct