Monthly rent was determined for each apartment in a random sample of 100 apartments. The sample mean was$820 and the sample standard deviation was $25. An approximate 95 percent confidence interval for the truemean monthly rent for the population of apartments from which this sample was selected is ($815, $825). Whichof the following statements is a correct interpretation of the 95 percent confidence level?(A) In this population, about 95 percent of all rental prices are between $815 and $825.(B) In this sample, about 95 percent of the 100 rental prices are between $815 and $825.(C) In repeated sampling, the method produces intervals that include the population mean approximately95 percent of the time.(D) In repeated sampling, the method produces intervals that include the sample mean approximately 95 percentof the time.(E) There is a probability of 0.95 that the true mean is between $815 and $825.

A random sample of 160 households is selected to estimate the mean amount spent on electric service. A 95% confidence interval was determined from the sample results to be ($151, $216). Which of the following is the correct interpretation of this interval? There is a 95% chance that the mean amount spent on electric service is between $151 and $216. We are 95% confident that the mean amount spent on electric service among the 160 households is between $151 and $216. 95% of the households will have an electric bill between $151 and $216. We are 95% confident that the mean amount spent on electric service among all households is between $151 and $216

A local councillor claims that the average weekly rent of a one-bedroom apartment is less than $200. A random sample of 45 one-bedroom apartments yielded a 95% confidence interval from $192 to $247 for the mean weekly rent. With reference to the above confidence interval, we can conclude that:Select one:a.the data support the councillor’s claim.b.the data contradict the councillor’s claim.c.the data do not contradict the councillor’s claim.d.there is evidence that the councillor’s claim is correct.

Suppose (35,40) is a 95% confidence interval estimate for a population mean 𝜇. Which of the following are true statements?I. There is a .95 probability that 𝜇 is between 35 and 40.II. If 100 random samples of the given size are picked and a 95% confidence interval is calculated from each, then 𝜇 will be in 95 of the resulting intervals.III. If 95% confidence intervals are calculated from all possible samples of the given size, 𝜇 will be in 95% of these intervals.I and III and IIIII and IIII, II, and IIINone of the above gives the complete set of true responses.

A student was asked to find a 95% confidence interval for weight of their backpacks in pounds using data from a random sample of size n = 20. Which of the following is a correct interpretation of the interval 3.1 < μ < 8.6? Assume the population is normally distributed.With 95% confidence, the weight of a randomly selected backpack will be between 3.1 and 8.6 pounds.There is a 95% chance that the mean of a sample of 20 backpacks will weigh between 3.1 and 8.6 pounds.There is a 95% chance that the weight is between 3.1 and 8.6.With 95% confidence, the mean weight of all backpacks is between 3.1 and 8.6 pounds.The sample mean weight of all backpacks is between 3.1 and 8.6 pounds, 95% of the time. We know this is true because the mean of our sample is between 3.1 and 8.6.

A student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 27. Which of the following is a correct interpretation of the interval 13.5 < μ < 22?Check all that are correct.There is a 98% chance that the mean of the population is between 13.5 and 22.With 98% confidence, the mean width of a randomly selected widget will be between 13.5 and 22.There is a 98% chance that the mean of a sample of 27 widgets will be between 13.5 and 22.With 98% confidence, the mean width of all widgets is between 13.5 and 22.The mean width of all widgets is between 13.5 and 22, 98% of the time. We know this is true because the mean of our sample is between 13.5 and 22.