In a recent interview, the producers of \"Big Brother\" claimed that one-third o

Question

In a recent interview, the producers of "Big Brother" claimed that one-third of the 15 to 24 age group regularly watch reality TVshows. A UQ academic wishes to test this claim. From a survey of 325 people in this age group, it was found that 126 regularly watched reality TV shows. Assume that the survey data were collected through a random sample and use a 5% alpha.

1. State the direction of the alternative hypothesis used to test the producers' claim. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.___________
2. Calculate the test statistic, reporting your answer to two decimal places.________
3. Use the tables in the textbook to determine the p-value for the test, giving your answer to four decimal places.___________
4. Is the null hypothesis rejected for this test? Type yes or no._________
5. Disregarding your answer for 4, if the null hypothesis was rejected, would the producers' claim appear to be valid at the 5% level? Type yes or no._________

Explanation / Answer

Proportion of the 15 to 24 age group who regularly watch reality TVshows p = 1/3

Null Hyp: H0: p = 1/3

Alt Hyp: Ha: p not = 1/3

Ans) ne

2) Sample proportion of the age group who regularly watched reality TV shows phat = 126/325

n = 325

Std error = sqrt[p * (1 - p) / n] = sqrt[1/3 * ( 1 - 1/3) / 325 ] = 0.026

Test stat = (phat - p) / SE = (126/325 - 1/3) / 0.026 = 2.08

3) p value for z = 2.079 is 0.0375

4) Since p value < 0.05 null is rejected

Ans) Yes

5) Yes

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