# A medical researcher says that

7.4.1 A medical researcher says that less than

83​%

of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of

200

80​%

think that healthy children should be required to be vaccinated. At

α=0.05​,

is there enough evidence to support the​ researcher’s claim? Complete parts​ (a) through​ (e) below.

​(a) Identify the claim and state

H0

and

Ha.

Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice.
​(Type an integer or a decimal. Do not​ round.)

B.

Find the critical​ value(s) and identify the rejection​ region(s).

Identify the critical​ value(s) for this test.

z0=
​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

​(c) Find the standardized test statistic z.

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

​(d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

the null hypothesis. There

enough evidence to

the​ researcher’s claim.

# A medical researcher says that

A medical researcher says that less than

76​%

of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of

500

73​%

think that healthy children should be required to be vaccinated. At

α=0.01​,

is there enough evidence to support the​ researcher’s claim? Complete parts​ (a) through​ (e) below.

​(a) Identify the claim and state

H0

and

Ha.

Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice.
​(Type an integer or a decimal. Do not​ round.)

A.

The percentage of adults in the country who think that healthy children should be required to be vaccinated is not

nothing​%.

B.

Less than

7676​%

of adults in the country think that healthy children should be required to be vaccinated.

C.

nothing​%

of adults in the country think that healthy children should be required to be vaccinated.

D.

More than

nothing​%

of adults in the country think that healthy children should be required to be vaccinated.

Let p be the population proportion of​ successes, where a success is an adult in the country who thinks that healthy children should be required to be vaccinated. State

H0

and

Ha.
​(b) Find the critical​ value(s) and identify the rejection​ region(s).

Identify the critical​ value(s) for this test.

Round to two decimal places as needed. Use a comma to separate answers as​ needed.)
Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) to complete your choice.
​(Round to two decimal places as​ needed.)

A.

The rejection region is

z<

B.

The rejection regions are

Z and
z>

C.

The rejection region is

z>

D.

The rejection region is

<z<.
​(c) Find the standardized test statistic z.

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