Question

A university conducted a study of online adults that included

405405

tablet owners. The study found that

213213

tablet owners use their tablet while watching TV. The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day. Complete parts​(a) through​ (d) below.

a. Use the​ five-step p-value approach to hypothesis testing and a

0.050.05

level of significance to try to prove that more than half of all tablet owners use their tablet while watching TV at least once per day. Determine the null​ hypothesis,

Upper H 0H0​,

and the alternative​ hypothesis,

Upper H 1H1.

Upper H 0H0​:

piπ

equals=

nothing

Upper H 1H1​:

piπ

greater than>

nothing

​(Type integers or decimals. Do not​ round.)

What are the level of​ significance,

alphaα​,

and sample​ size, n?The level of significance is

nothing.

The sample size is

nothing.

​(Type integers or decimals. Do not​ round.)

Determine the appropriate sampling distribution and test statistic. Select the correct choice below​ and, if​necessary, fill in the answer box to complete your choice.

A.Use the normal distribution and the

Upper Z Subscript STATZSTAT

test statistic.

B.Use the t distribution with

nothing

degrees of freedom and the

t Subscript STATtSTAT

test statistic.

Determine the test statistic.

The test statistic is

nothing.

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

Determine the​ p-value.

The​ p-value is

nothing.

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

State the conclusion.

▼

Reject

Do not reject

the null hypothesis. There

▼

is not

is

sufficient evidence to conclude that the proportion of tablet owners who use their tablet while watching TV at least once per day is

▼

not equal tonot equal to

equal toequal to

less thanless than

greater thangreater than

nothing.

​(Type an integer or a decimal. Do not​ round.)

b. Based on the result in part​ (a), is the claim implied by the authors​ valid?

The claim

▼

is not

is

valid. There

▼

is not

is

sufficient evidence to conclude that more than half of all tablet owners use their tablet while watching TV at least once per day because the​ p-value is

▼

greater thangreater than

less thanless than

the level of significance.c. Suppose the study found that

240240

tablet owners use their tablet while watching TV at least once per day. Repeat parts​ (a) and​ (b). What is the test​ statistic?The test statistic is

nothing.

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

Determine the​ p-value.

The​ p-value is

nothing.

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

What is the final​ conclusion?

▼

Reject

Do not reject

the null hypothesis. The claim

▼

is

is not

valid. There

▼

is

is not

sufficient evidence to conclude that more than half of all tablet owners use their tablet while watching TV at least once per day because the​p-value is

▼

greater thangreater than

less thanless than

the level of significance.

d. Compare the results of parts​ (b) and​ (c).

The results of part​ (b) are

▼

the same as

different from

the results of part​ (c). Adding additional tablet owners that use their tablet while watching TV

▼

increases

does not change

decreases

the possibility that more than half of all tablet owners use their tablet while watching TV at least once per day.

Answer 1

1)

Determine the null​ hypothesis and the alternative​ hypothesis,

The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day.

I.e P > 0.5

Ho : P = 0.5 vs Ha: P > 0.5

2)

What is the level of​ significance,

α =0.05

sample​ size, n = 405

3)

Determine the appropriate sampling distribution and test statistic.

A.Use the normal distribution and the

Zstat  test statistic.

4)

Reject the null hypothesis.

The claim is valid.

There is sufficient evidence to conclude that more than half of all tablet owners use their tablet while watching TV at least once per day because the​ p-value is less than the level of significance.

Compare the results of parts​ (b) and​ (c).

The results of part​ (b) are different from the results of part​ (c).

Adding additional tablet owners that use their tablets while watching TV increases the possibility that more than half of all tablet owners use their tablets while watching TV at least once per day.