Question

# A poll of 2,133 randomly selected adults showed that 94​% of them own cell phones. The...

A poll of 2,133 randomly selected adults showed that 94​% of them own cell phones. The technology display below results from a test of the claim that 92​% of adults own cell phones. Use the normal distribution as an approximation to the binomial​ distribution, and assume a 0.01

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

 Test of pequals

0.92vs

pnot equals

0.92

Sample

X

N

Sample p

​95% CI

​Z-Value

​P-Value

1

1996

2 comma 133

0.935771

​(0.922098​,0.949444

 ​) 2.68

0.007

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

​Left-tailed test

​Two-tailed test

Right tailed test

b. What is the test​ statistic?

The test statistic is

.​(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.

Upper H 0 : p less than 0.92

B.

Upper H 0 : p equals 0.92

C.

Upper H 0 : p not equals 0.92

D.

Upper H 0 : p greater than 0.92

A.

Reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

alpha

.

B.

Fail to reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

alpha

.

C.

Reject the null hypothesis because the​ P-value is

greater than

the significance​ level,

alpha

.

D.

Fail to reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

alpha

.

e. What is the final​ conclusion?

A.

There

is not

sufficient evidence to warrant rejection of the claim that

92

​%

of adults own a cell phone.

B.

There

is not

sufficient evidence to support the claim that 92% of adults own a cell phone.

C.There is sufficient evidence to support the claim that 92% of adults own a cell phone.

D.There is sufficient evidence to warrant rejection of the claim that 92%

of adults own a cell phone.

Solution :

a) This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.92

Ha : p 0.92

= 0.94

n = 2133

P0 = 0.92

1 - P0 = 1 -0.92 = 0.08

b) Test statistic = z

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

=0.94 -0.92 / [0.92*(0.08) /2133 ]

= 3.40

c) P(z >3.40 ) = 1 - P(z <3.40 ) = 0.0003

P-value = 0.000

= 0.01

0.0003 < 0.01

Reject

d)B.Upper H 0 : p equals 0.92

A.Reject the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

alpha

e) C.There is sufficient evidence to support the claim that 92% of adults own a cell phone.

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