QUESTION 4 A member of the Islip Urban Renewal Taskforce claimed that more than

Question

QUESTION 4 A member of the Islip Urban Renewal Taskforce claimed that more than three quarters of new homes in the region were built with family rooms. 1. State the direction of the alternative hypothesis used to test the taskforce claim. Type gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. Another committee member, who did not originally believe the claim, took a random sample of 84 houses in the area to test the validity of the claim. He found that 78 of them had family rooms. 2 Use the tables in the textbook to determine the critical value of the test statistic using a 3% level of significance. If there are two critical values, state only the positive value. 3. Calculate the test statistic, correct to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that more than three quarters of new homes in the region were built with family rooms at the 3% level of significance? Type yes or no.

Explanation / Answer

Solution1:

H0;p=3/4

H1:p>3/4

since claim it is written more than

greater than or equal to

Solution2:

alpha=0.03

alpha/2=0.03/2

=0.017

Using TI 83 calc

2.170

ANSWER:CRITICAL VALUE=2.17

Solution3:

Z=p^-p/sqrt(p(1-p)/n

p^=sample proportion=x/n=78/84=0.928571

Z=0.928571-0.75/sqrt(0.75(1-0.75)/84)

Z=3.78

test statistic=3.78

SOlutiuon4:

test statistic>critical vlaue

Reject Null hypothesis.

YES

Solution5:

YES

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