Question

In: Statistics and Probability

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 StatCrunch or TI-83/84 calculator to do these calculations but be sure to include the printout in your post.

Solutions

Expert Solution

By using the TI-84 Calculator we have to solve this question.

Claim: The proportion of zeroes is not equal to 0.1

The null and alternative hypothesis is

H0: P = 0.1

H1: P 0.1

Level of significance = 0.01

Sample size = n = 1500

x = 225

The TI-84 calculator path is Click on STAT --------->TESTS -------->1-PropZTest------->

P0: 0.1

x: 225

n: 1500

prop: p0

Calculate

We get

z = 6.46

P-value = 0.0000

P-value < 0.01 we reject null hypothesis.

Conclusion:

The proportion of zeroes is not equal to 0.1

Now we have to construct a 99% confidence interval to estimate the proportion of zeroes.

TI-84 Calculator path is Click on STAT --------> TESTS ---------> 1-PropZInt --------->

x: 225

n: 1500

C-Level: 0.99

Calculate

We get

So the confidence interval is (0.1263, 0.1738)

The value 0.1 does not belong to the above interval so we reject the null hypothesis.

Both results are the same.

orchestra answered 2 years ago
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