Question

(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

​(b) Find the critical​ value(s) and identify the rejection​ region(s). (c) Find the standardized test statistic.​ (d) Decide whether to reject or fail to reject the null hypothesis.In a sample of

10001000

home​ buyers, you find that

431431

home buyers found their real estate agent through a friend. At

alphaαequals=0.020.02​,

can you reject the claim that

4040​%

of home buyers find their real estate agent through a​ friend?

​(a) Which of the following correctly states

Upper H 0H0

and

Upper H Subscript aHa​?

A.

Upper H 0H0​:

pequals=0.400.40

Upper H Subscript aHa​:

pgreater than>0.400.40

B.

Upper H 0H0​:

pgreater than or equals≥0.400.40

Upper H Subscript aHa​:

pless than<0.400.40

C.

Upper H 0H0​:

pless than or equals≤0.400.40

Upper H Subscript aHa​:

pgreater than>0.400.40

D.

Upper H 0H0​:

pgreater than>0.400.40

Upper H Subscript aHa​:

pless than or equals≤0.400.40

E.

Upper H 0H0​:

pequals=0.400.40

Upper H Subscript aHa​:

pnot equals≠0.400.40

F.

Upper H 0H0​:

pless than<0.400.40

Upper H Subscript aHa​:

pgreater than or equals≥0.40

Identify H0 And Ha.

H0​:p

Ha​:p

​(Type integers or​ decimals.)

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

The critical​ value(s) is/are

z 0=    .

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

(b) What is​ (are) the critical​ value(s) of z0​?

z 0=

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

Which of the following graphs has the rejection​ region(s) shaded​ correctly?

​(c) What is the standardized test​ statistic?

zequals=

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

​(d) Which of the following is the correct conclusion for the​ test?

A.

RejectReject

Upper H 0H0.

There

is notis not

enough evidence to reject the claim that

49 %49%

of buyers find their real estate agent through a friend.

B.

RejectReject

Upper H 0H0.

There

isis

enough evidence to reject the claim that

49 %49%

of buyers find their real estate agent through a friend.

This is the correct answer.

C.

Fail to rejectFail to reject

Upper H 0H0.

There

is notis not

enough evidence to reject the claim that

49 %49%

of buyers find their real estate agent through a friend.

D.

Fail to rejectFail to reject

Upper H 0H0.

There

isis

enough evidence to reject the claim that

49 %49%

of buyers find their real estate agent through a friend.

Answer 1

A) H₀: P = 0.40

H₁: P 0.40

B) At alpha = 0.02 the critical values are +/- z_0.01 = +/- 2.33

C) The test statistic z = (p - P)/sqrt(P(1 - P)/n)

= (0.431 - 0.4)/sqrt(0.4 * 0.6/1000)

= 2

D) Since the test statistic value is not greater than the upper critical value (2 < 2.33), so we should not reject the null hypothesis.

Option - C) Fail to reject H0. There is not enough evidence to reject the claim that 40% of buyers find their real estate agent through a friend.