Question

A medical researcher says that less than

88​%

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

500

adults in that​ country,

85​%

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 ____​%

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

C.Less than ___%of adults in the country think that healthy children should be required to be vaccinated.

D.More than __% 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

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

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

z0 =___

Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(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.

▼

Reject

Fail to reject

the null hypothesis. There

▼

is

is not

enough evidence to

reject

support

the​ researcher's claim.

and

Upper H Subscript aHa.

Select the correct choice below and fill in the answer boxes to complete your choice.

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

Answer 1

A)

Claim is C.Less than __88_%of adults in the country think that healthy children should be required to be vaccinated

B)

N = 500

P = 0.88

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 440

N*(1-p) = 60

Both the conditions are met so we can use standard normal z table to conduct the test

From z table, P(z<-2.33) = 0.01

So, critical value is = -2.33

And rejection region is less than -2.33

C)

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Claimed p = 0.88

Observed P = 0.85

N = 500

Z = -2.06

D)

As -2.06 is not less than -2.33

We fail to reject Ho

There is not enough evidence to support the claim.