Question

A major Blu-ray rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players. The value of the test statistic in this problem is approximately equal to ____
(A) 2.8
(B) 2.6
(C) 1.3
(D) 1.94

Answer 1

Answer: (A) 2.8

Step-by-step explanation:

Given : The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players.

i.e. Population proportion : $p=\dfrac{5000}{20000}=0.25$

Also, It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players.

i.e. Sample proportion : $\hat{p}=\dfrac{96}{300}=0.32$

Test statistic for proportion:

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

i.e  $z=\dfrac{0.32-0.25}{\sqrt{\dfrac{0.25\cdot0.75}{300}}}=2.8$

Thus, the value of the test statistic in this problem is approximately equal to 2.8

Hence, the correct answer is option (A).