Question

When analyzing the last digits of telephone numbers in Sandtown, it was found that among 1500...

When analyzing the last digits of telephone numbers in Sandtown, it was found that among 1500 randomly selected phone numbers, 225 had zero as the last digit. If the digits are selected randomly, the proportion of zeroes should be 0.1 because from probability, 0 is one of the 10 possible digits.

  1. Use the p-value method with a 0.01 level of significance to test the claim that the proportion of zeroes is not equal to 0.1.
  2. Use the sample data to construct a 99% confidence interval to estimate the proportion of zeroes. What does the    confidence interval suggest about the claim that the proportion of zeroes is 0.1?
  3. Compare the results from the hypothesis test and confidence interval. Do they lead to the same conclusion? Why or why not?

You may use TI-84 calculator, or any software you prefer to do these calculations but be sure to include the printout

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Let assume the actual the proportion of zeroes be .

we need to check whether  the proportion of zeroes is not equal to 0.1.

So here the hypothesis are

.

Here the test statistic is

so the p-value of the test is

So at level of significance 0.1 we reject null hypothesis as p-value<0.1.So there is enough evidence to conclude the proportion of zeroes is not equal to 0.1.

For calculating the exact 99% confidence interval we use MINITAB software.

and get the confidence interval as (0.127065, 0.175194).

Clearly in 0.1 does not belong to this interval so our conclusion is correct.

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