Confidence Intervals

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1. 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

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2. Find the critical value for zα/2 that corresponds to a degree of confidence of 98%.

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3. Find the margin of error for the 95% confidence interval used to estimate the population proportion with n = 163 and x = 96.

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4. Construct the confidence interval for question 3.

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5. Interpret the confidence interval found in question 4.

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6. What are the requirements for a Student’s t-distribution?

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7. Find the critical value for tα/2 corresponding to n = 12 and 95% confidence level.

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8. Use the confidence level and sample data to find the margin of error E.

College students’ annual earnings:

99% confidence, n = 81, = $3967, s = $874

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9. Construct the confidence interval for question 8 above.

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10. Interpret and describe the confidence obtained in question 9 in non-technical terms.

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