Margin of Error and Confidence Interval - Homework

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.

Suppose that a confidence interval for hours worked by students was computed to be (8.82, 10.78). Which of these is a valid interpretation of this confidence interval?

• There is a 95% probability that the mean number of hours worked by all students is between 8.82 and 10.78 hours.

• There is a 95% probability that a randomly selected student worked between 8.82 and 10.78 hours.

• We are 95% confident that the population mean number of hours worked by all students is between 8.82 and 10.78 hours.

• We are 95% confident that the mean number of hours worked by the students in our sample is between 8.82 and 10.78 hours.

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

• Yes

• No

• Not enough information

• I have no idea what you're asking of me

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%.

1. A 95% confidence level means...

• A. There is a 95% probability that the true population parameter falls within the interval.

• B. There is a 5% probability that the true population parameter falls within the interval.

• C. If we were to repeat the sampling process many times, 95% of the intervals constructed would contain the true population parameter.

2. A confidence level is:

• A. The probability that the true population parameter falls within the interval.

• B. The probability that the sample mean falls within the interval.

• C. The level of confidence we have that the interval contains the true population parameter.

• D. The margin of error for the estimate.

The lifespan of a certain brand of car tires is approximately normally distributed. The car tires have a mean lifespan of 60,000 miles and a standard deviation of 7,000 miles.

What range of​ car-tire lifespan contains the 95​% closest to the mean?

• 59,000 to 61,000 miles

• 53,000 to 67,000 miles

• 46,000 to 74,000 miles

• 39,000 to 81,000 miles

Assume that population means are to be estimated from the samples described.

Use the sample results to approximate the 95% confidence interval.

sample mean = 85​, sample standard deviation = .9

• 85, 169

• 83.2, 86.8

• 82.2, 87.8

• 80.8, 89.2

A group of students was trying to determine the proportion of candies in a bag that are blue. The company claims that 24% of candies in bags are blue. A simulation was run 100 times with a sample size of 50, based on the premise that 24% of the candies are blue. The approximately normal results of the simulation are shown in the dot plot below.

The simulation results in a mean of 0.254 and a standard deviation of 0.060. Based on this simulation, what is a plausible interval containing the middle 95% of the data?

• (0.194, 0.314)

• (0.134, 0.374)

• (−0.448, 0.568)

• (0.254,0.374)

Mary bought a pack of candy. The manufacturer claims that 30% of the candies manufactured are red. In her pack, 14 of the 60 candies are red. She ran a simulation of 300 samples, assuming the manufacturer is correct. The results are shown below.
Based on the simulation, Mary determines that the middle 95% of plausible values that the proportion of red candies in a pack is 0.185 to 0.417. Based on the simulation, is it unusual that Mary’s pack had 14 red candies out of a total of 60?

• Yes, it is unusual that Mary's pack had 14 red candies out of 60 candies.

• No, it is not unusual that Mary's pack had 14 red candies out of 60 candies.