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aalyn [17]
3 years ago
15

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. Ho

w many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the​ Internet? Assume that we want to be 90​% confident that the sample percentage is within five percentage points of the true population percentage for all sales transactions.
Mathematics
1 answer:
sleet_krkn [62]3 years ago
4 0

Answer:

We need at least 271 transactions

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

Minimum sample size within five percentage points.

n when M = 0.05.

We dont know the proportion, so we use \pi = 0.5, which would be the proportion requiring the largest sample size

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.645\sqrt{\frac{0.5*0.5}{n}}

\0.05\sqrt{n} = 1.645*0.5

\sqrt{n} = 16.45

(\sqrt{n})^{2} = (16.45)^{2}

n = 270.6

Rouding up

We need at least 271 transactions

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