A media ad indicates that 60% of adults use a tax service to fill out their taxe

Question

A media ad indicates that 60% of adults use a tax service to fill out their taxes. Linda believes that true value is lower than stated in the news report. Linda obtains a random sample of 250 adults and finds that 130 use a tax service to fill out their taxes. Does this support Linda's claim at a 5% level of significance?

1. The parameter for this scenario is: which is correct

A. The mean age among all tax service providers

B. The proportion of all adults who ask Linda to fill out their taxes

C. The proportion of all adults who use a tax service to fill out their taxes

D. The proportion of all adults who file taxes

2. Which is the correct set of hypotheses?

A. H0:p=60 vs HA:p is different than 0.60

B. H0:p<0.60 vs HA:p=0.60

C. H0:p=0.60 vs HA:p<0.60

D. H0:p=0.60 vs HA:p>0.60

3. Decision rule: reject H0 if the p-value is less than or equal to _. Give as decimal.

4. The sample proportion is calculated to be _ when rounded to three digits after the decimal point. Then the calculated value of the test statistic when rounded to two digits after the decimal point is _.

5. Based on the test statistic value and the alternative hypothesis, the p-value is _ when rounded to three digits after the decimal.

6. The correct decision it to: reject H0 or fail to reject H0?

7. Write an appropriate summary based on the findings.

Explanation / Answer

1. Correct answer: Option (C)

2. Correct answer: Option (C)

3. reject H0 if the p-value is less than or equal to 0.05

4. Sample proportion p = 130/250 = 0.52
Test statistic Z = (p - P) / Sqrt(PQ/n) = (0.52-0.60) / Sqrt(0.60*0.40/250) = -2.582

5. P-Value: 0.0049

6. Here P-value < alpha 0.05, so we reject H0

7. we conclude that true value is lower than stated in the news report

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