Confidence Intervals

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants.

The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

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

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]

A nutritionist found that in a sample of 80 families, 22% said they are apples at least once a week. Construct the 90% CI for the population proportion.

• (0.144, 0.296)

• (0.190, 0.250)

• (0.704, 0.856)

• (0.129, 0.311)

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.

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

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.

Find the critical value.

• 0.90

• 1.155

• 1.645

• ±1.645

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

• 7.72 < μ < 12.40

• 12.40 < μ < 7.72

_______ is a part of a group being surveyed.

• Sample

• Population

• Random Sample

• Quartile

_______ is the entire group of objects or individuals considered for a survey.

• Sample

• Population

• Random Sample

• Quartile