11.3 Confidence Intervals

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For an IQ the mean is 100, the standard deviation is 10. Determine the z score of someone who got 70.

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For an IQ the mean is 100, the standard deviation is 10. Determine the z score of someone who got 120.

Multiple Choice

For an IQ the mean is 100, the standard deviation is 10. Assuming it is normally distributed, 95% of results should fit between...

• 80.4 and 119.6

• 80 and 120

• 90.4 and 110.6

• 70 and 130

​Z score reminder

99% - 2.58
95% - 1.96
90% - 1.645

Multiple Choice

For an IQ the mean is 100, the standard deviation is 10. Assuming it is normally distributed, 99% of results should fit between...

• 60.3 to 140.7

• 74.2 to 125.8

• 65.1 to 135.9

Multiple Choice

For an IQ the mean is 100, the standard deviation is 10. Assuming it is normally distributed, 99% of results should fit between...

• 80 to 120
• 74.24 to 125.76
• 60 to 140
• 90 to 110

​lie

Multiple Choice

What does a 90% confidence interval indicate about the population mean?

• It means the population mean will always be in the interval.

• It means 90% of the possible samples will have the population mean in the calculated interval.

• It means the sample mean is always equal to the population mean.

• It means the interval is 90% of the sample size.

Multiple Choice

Which of the following z-scores would you use for a 99% confidence interval?

• ±1.645

• ±1.96

• ±2.58

• ±2.33

Multiple Choice

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

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A sample of 20 cupcakes found the interval for average calories to be (150, 350) with 95% confidence. What percentage of cupcakes could be estimated to have over 350 calories?

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After surveying 20 people, you find the average lunch spending is $4.53 with a standard deviation of $0.23. State the 95% confidence interval for the average amount spent on lunch today.

Open Ended

In Worked Example 3, the average amount spent on lunch was between $4.43 and $4.63. Determine the sample size needed to reduce the interval to ±$0.05 for a 95% confidence interval.

Fill in the Blanks

...average vegetable consumption?