t intervals

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 true mean caloric content of cupcakes is between 150 and 350 calories.

• We are 95% confident that a sample of 20 cupcakes will find between 150 and 350 calories per cupcake.

• None of these are correct.

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CCSS.HSS.IC.B.4

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 from which the sample was gathered.

• 89.08 < μ < 94.92

• 87.27 < μ < 96.73

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

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CCSS.HSS.IC.B.4

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

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CCSS.HSS.IC.B.4

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.52, 125.6)

• (112.8, 127.4)

• (112.52, 127.68)

• (114.56, 125.64)

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CCSS.HSS.IC.B.4

The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 13.2,  5.1,  7.5,  8.0,  12.7,  7.6,  13.8,  14.5,  7.7, and 10.5.  Determine a 95 percent confidence interval for the mean time for all players.

• 12.30 < μ < 7.82

•  7.82 < μ < 12.30

• 7.70 < μ < 12.42

• 12.40 < μ < 7.72

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CCSS.HSS.IC.B.4

Construct a 90% confidence interval of a random sample size of 19 cows with a mean of 155.526 and a standard deviation of 19.993. 

• (146.54, 164.52)
• (147.57, 163.48)
• (147.59, 163.46)
• (143.69, 167.36)

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CCSS.HSS.IC.B.4

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Calculate the confidence interval.

• 103 to 107

• 100 to 105

• 99.5 to 105

• 98.7 to 106

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CCSS.HSS.IC.B.4

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.

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CCSS.HSS.IC.B.4

Compute a 90% confidence interval for the situation:

A random sample of 30 movie theaters showed that the average price for a movie was $10 with a standard deviation of $1.20.

• (9.71, 10.29)

• (9.934, 10.066)

• (9.64, 10.36)

• (9.628, 10.372)

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CCSS.HSS.IC.B.4

Compute a 98% confidence interval:

Last year, the times for Midlo soccer games were normally distributed with a standard deviation of 2.8 minutes. A random sample of 7 soccer games this year had an average length of 94 minutes.

• (91.235, 96.765)

• (91.827, 96.173)

• (91.538, 96.462)

• (90.674, 97.326)

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CCSS.HSS.IC.B.4