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.

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