Knowee
Questions
Features
Study Tools

In which of the following scenarios can we calculate a confidence interval for the population mean? Check all that apply. A random sample of 60 cell phone calls is selected and the mean length of calls is determined to be 3.25 minutes with a standard deviation of 4.2 minutes. A random sample of 15 women athletes is selected and their mean weight is determined to be 136 pounds. Female athlete weights are known to be normally distributed with a population standard deviation of 20 pounds. A random sample of 14 cell phone calls is selected and the mean length of calls is determined to be 3.25 minutes with a standard deviation of 4.2 minutes. A random sample of 35 women athletes is selected and their mean weight is determined to be 136 pounds. Female athlete weights are known to be normally distributed with a population standard deviation of 20 pounds.

Question

In which of the following scenarios can we calculate a confidence interval for the population mean? Check all that apply. A random sample of 60 cell phone calls is selected and the mean length of calls is determined to be 3.25 minutes with a standard deviation of 4.2 minutes. A random sample of 15 women athletes is selected and their mean weight is determined to be 136 pounds. Female athlete weights are known to be normally distributed with a population standard deviation of 20 pounds. A random sample of 14 cell phone calls is selected and the mean length of calls is determined to be 3.25 minutes with a standard deviation of 4.2 minutes. A random sample of 35 women athletes is selected and their mean weight is determined to be 136 pounds. Female athlete weights are known to be normally distributed with a population standard deviation of 20 pounds.

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

We can calculate a confidence interval for the population mean in the following scenarios:

  1. A random sample of 60 cell phone calls is selected and the mean length of calls is determined to be 3.25 minutes with a standard deviation of 4.2 minutes. This scenario meets the criteria because the sample size is large enough (n > 30) to apply the Central Limit Theorem, which allows us to assume a normal distribution.

  2. A random sample of 15 women athletes is selected and their mean weight is determined to be 136 pounds. Female athlete weights are known to be normally distributed with a population standard deviation of 20 pounds. This scenario meets the criteria because even though the sample size is small (n < 30), we know that the population is normally distributed and we know the population standard deviation.

  3. A random sample of 35 women athletes is selected and their mean weight is determined to be 136 pounds. Female athlete weights are known to be normally distributed with a population standard deviation of 20 pounds. This scenario meets the criteria because the sample size is large enough (n > 30) to apply the Central Limit Theorem, which allows us to assume a normal distribution.

The scenario where a random sample of 14 cell phone calls is selected and the mean length of calls is determined to be 3.25 minutes with a standard deviation of 4.2 minutes does not meet the criteria because the sample size is too small (n < 30) and we do not know if the population is normally distributed.

This problem has been solved

Similar Questions

Assuming data come from a random sample, under which of the following conditions should we not calculate a confidence interval for a population mean? Population distribution is unknown and sample size is 50 individuals. Population distribution is unknown and sample size is 20 individuals. Population is normally distributed and sample size is 20 individuals. Population is normally distributed and sample size is 50 individuals.

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 study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours. The 95% confidence interval for the mean, μ, is (7.7, 9.3).Which of the following will provide a more informative (i.e., narrower) confidence interval than the 95% confidence interval? Check all that apply. Using a sample of size 400 (instead of 81) Using a sample of size 36 (instead of 81) Using a different sample of size 81 Using a 90% level of confidence (instead of 95%) Using a 99% level of confidence (instead of 95%)

A study was conducted to estimate μ, the mean commute distance that all employed U.S. adults travel to work. Suppose a random sample of 49 employed U.S. adults gives a mean commute distance of 22 miles and that from prior studies, the population standard deviation is assumed to be σ = 8.4 miles.How large a sample of U.S. adults is needed in order to estimate μ with a 95% confidence interval of length 2.4 miles? 111 49 196 784

Juana is interested in estimating how long it takes students at her school to complete a maze she designed. She takes a random sample of   students and records how long it takes each of them to complete the maze. They work separately from each other, so Juana is willing to assume independence. Here are the data with summary statistics:Player     Time (minutes)     Mean   seconds Standard deviation   seconds Assume that all conditions for inference are met for this sample.Which of the following is a   confidence interval for the mean time (in seconds) it takes students to complete this maze?Choose 1 answer:Choose 1 answer:(Choice A)    A  (Choice B)    B  (Choice C)    C  (Choice D)    D (Choice E)    E

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.