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StatisticsQ&A LibraryUsing Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.a. Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.b. Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.c. Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?d. Compare the results from the critical value method, the value method, and the confidence interval method. Do they all lead to the same conclusion?Question

Asked Jan 13, 2020

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Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a. Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b. Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c. Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d. Compare the results from the critical value method, the value method, and the confidence interval method. Do they all lead to the same conclusion?

Step 1

a)

The null and alternative hypothesis stated below:

Null hypothesis H_{0}: P = 0.1.

Alternative hypothesis H_{1}: P ≠ 0.1.

The sample proportion is obtained below:

Step 2

The test statistics z is obtained below:

Step 3

At alpha = 0.05, the critical values are z0.025 = +/- 1.96

**Conclusion:**

Since the test statistic value is greater than the upper critical value (2 > 1.96), so we should reject the null hypothesis.

So at 0.05 significance level, there is not sufficient evidence to support the claim that the proportion of zeros equals 0.1.

b)

The P-value is obtained below:

P-value = 2 * P(Z > 2)

= 2 * (1 - P(Z < 2))

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