Confidence Interval

Confidence Intervals of Proportions

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Definitions:

Confidence Interval- An interval estimate for an unknown population parameter. This depends on: (1) the desired confidence level, (2)information that is known about the distribution (for example, known standard deviation), (3) the sample and its size.

z-score - gives the number of standard deviations a value is away from the mean.

Calculating Confidence Intervals

Understanding and calculating confidence intervals for population proportions - statistics help

An optional youtube video is included on the next slide.

Url: https://youtu.be/OkR3PkT15uM

Understanding and calculating confidence intervals for population proportions - statistics help (optional youtube video)

Multiple Choice

Which of the following values below represents the critical value for a 98% confidence interval?

• 2.326

• 2.054

• 1.645

• 3.091

Multiple Choice

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144
• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 
• 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144
• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

Multiple Choice

A researcher at a major hospital wishes to estimate the proportion of the adult population of the U.S. that has high blood pressure.  How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

• 9
• 271
• 164
• 542

Multiple Choice

Which of the following actions would produce a confidence interval with a smaller width assuming all other contingencies remained constant?

• Using a higher confidence level

• Using a lower confidence level

Multiple Choice

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

Example 1

Multiple Choice

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?

• (0.621, 0.780)

• (0.591, 0.812)

• (0.584, 0.830)

• (0.615, 0.805)

Multiple Choice

A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

Multiple Choice

A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?

• 0.001 < p < 0.005

• 0.566 < p < 0.693

• 0.148 < p < 0.252

• 0.023 < p < 0.045

Multiple Choice

If 827 represents "no" voters out of 2584, construct a 95% confidence interval for the "no" group.

• [.300,.340]
• [.298,.342]
• [.302,.338]
• [.288,.352]

Example 2

Multiple Choice

A preliminary study suggests that 87% of people agree on an issue. How large must your sample size be so you could be within ± 3% of p calculate at 90% confidence?

• 7

• 466

• 5

• 338

Multiple Choice

A preliminary study suggests that 87% of people agree on an issue. How large must your sample size be so you could be within ± 3% of p calculate at 90% confidence?

• 7

• 466

• 5

• 338

Multiple Choice

A preliminary study suggests that 17% of people agree on an issue. How large must your sample size be so you could be within ± 5% with 95% confidence?

• 217

• 30

• 2

• 152