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.

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