Question

(a) Write the claim mathematically and identify H0 and Ha.

​(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 1797 home​ buyers, you find that 785 home buyers found their real estate agent through a friend. At α=0.06​, can you reject the claim that 43​% of home buyers find their real estate agent through a​ friend?

​(a) Which of the following correctly states H0 and H Ha​?

H0​: p = 0.43

Ha​: p ≠ 0.43

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

z0= −1.88, 1.88

(c) What is the standardized test​ statistic?

z= ____

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

(d) Decide whether to reject or fail to reject the null hypothesis. Reject or Fail to reject? is or is not enough evidence? Support or Reject?

Answer 1

Here we have given that,

Claim: To check whether the Population proprotion is not equal to 0.43 (43%).

The Hypothesis is

v/s

Now,

n=number of home buyers=1797

x: number of home buyers found their real estate agent through friend=785

Now, we estimate the proportion p as

=sample proportion =

Test statistic:

=0.58

we get

Test statistics = 0.58

Now we find the Critical value

= level of significance= 0.06

Zcritcal == -1.88 Using Excel=NORMSINV(prob=0.06/2)

Decision:

Here Zstatistics > Z-critical

i.e we Reject Ho(Null Hypothesis)

Conclusion:

There is sufficient evidence that the Population proprotion is not equal to 0.43.