1718 Confidence Intervals with Means A

A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a standard deviation of $47.5. Which of the following would be the 98% confidence interval for the mean money spent by all visitors to this theme park?

• ($130.77, $153.23)

• ($132.77, $151.43)

• ($132.69, $151.31)

• ($140.88, $143.12)

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CCSS.HSS.IC.B.4

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The sample size is too small for a z-distribution
• Clarity ratings for the entire bacth are normally distributed.  
• The t-distribution will create a narrower interval than z.
• The standard deviation for the batch is unknown.

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CCSS.HSS.IC.B.4

A biologist has taken a random sample of a specific type of fish from a large lake. A 95 percent confidence interval was calculated to be 6.8 ± 1.2 pounds. Which of the following is true? 

• 95 percent of all the fish in the lake weigh between 5.6 and 8 pounds. 
• In repeated sampling, 95 percent of the sample proportions will fall within 5.6 and 8 pounds.
• In repeated sampling, the population mean fish weight will be captured in the interval 95% of the time. 
• There is a 95% chance that the population mean weight is 6.8 pounds.

A researcher wishes to determine the mean energy consumption of a new light bulb. She takes a random sample of 41 bulbs and determines that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7. When constructing a 97% confidence interval, which would be the most appropriate value of the critical value?  

• 2.072
• 2.25
• 2.704
• 2.807

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students.

• 89.08 < μ < 94.92 
• 87.27 < μ < 96.73
• 87.29 < μ < 96.71 
• 87.77 < μ < 96.23

The 90% interval for a statistics test was given by 72 +- 7. What is the lower bound for the interval?

• 7
• 72
• 65
• 79

Which of the following does NOT have an affect on the width of a confidence interval?

• Sample mean
• t*
• Sample standard deviation
• Sample size

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CCSS.HSS.IC.B.4

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.

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CCSS.HSS.IC.B.4

A 90% confidence interval for the mean speed driven by cars on East Main St. is given by (21, 45). What was the sample mean of this study?

• 12
• 24
• 33
• None of these.

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

• We are 95% confident that the true mean calorie content can be found with a sample of 150 to 350 cupcakes.
• We are 95% confident that the true mean calorie content in cupcakes is between 150 and 350 calories.
• 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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CCSS.HSS.IC.B.4