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)2.80.
B)2.60.
C)1.94.
D)1.30.

Question

Quizplus · Accepted Answer

First we need to calculate the sample proportion, which is 96/300 = 0.32.
Then we need to calculate the standard error, which is the square root of [(0.32)(0.68)/300] = 0.033.
Next, we calculate the test statistic, which is (0.32-0.25)/0.033 = 2.12 (rounded to two decimal places).
Since we are testing for a value greater than 0.5, this is a one-tailed test. With 298 degrees of freedom (300-2), the critical value for alpha = 0.05 is 1.645. Since our test statistic (2.12) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. Therefore, the chain should open the new store. The closest answer choice is A) 2.80, which is a reasonable approximation given the rounding done in the calculation of the test statistic.

A Major Blu-Ray Rental Chain Is Considering Opening a New