### Educational Website: Sampling Distribution Exercise---#### Sampling Distribution**Instructions:**Suppose the mean number of people attending all 2017 Veterans Day celebrations held in Virginia is 182 with a standard deviation of 37 people. A few of the celebrations are huge, and hence the distribution is skewed heavily to the right. If a simple random sample of 54 Veterans Day celebrations held in Virginia is selected and the number of people in attendance is determined for each, describe completely the sampling distribution of the resulting mean number of people attending for this sample of 54 Veterans Day celebrations held in Virginia.---**Question 21: Minimum Sample Size for Sampling Distribution****What is the minimum sample size needed to describe the distribution of the sample mean for this problem?**- [ ] 40 or more- [x] Any size will work- [ ] 15 or more---**Question 22: Application of the Central Limit Theorem****Is the sample size large enough to apply the Central Limit Theorem?**- [ ] No- [x] Yes---**Question 23: Center of the Sampling Distribution****What is the center of the sampling distribution of the mean?**- [ ] 4.318- [ ] 156- [ ] 5.035- [x] 182- [ ] 134- [ ] 3.335---### Explanation:**Central Limit Theorem (CLT):** For sufficiently large sample sizes (n > 30), the distribution of the sample mean will be approximately normal, irrespective of the shape of the population distribution.**Center of Sampling Distribution:** The mean of the sampling distribution (also called the expected value of the sample mean) is equal to the mean of the population (μ).In this case:- Population mean (μ) = 182- Given a sample size (n) = 54, which is large enough for the CLT to apply.Thus:- The sampling distribution of the sample mean will be approximately normal.- The center (mean) of this sampling distribution is 182.

here given , Suppose the mean number of people attending all 2017 Veterans Day celebrations held in…

Answered: Suppose the mean number of people…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Illinois and Massachusetts. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the state of Illinois is greater than the mean annual income of childcare workers in Massachusetts. To see if this is true, the firm selected random sample of 25 childcare workers from Illinois and an independent random sample of 25 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 45679, 47412, 38478, 44646, 44364, 45265, 41423, 45861, 45936, 34016, 43020, 4960o8, 43710, 45738, 41546, 38681, 34889, 39468, 45463, 53593, 40847, 38255, 45708, 57662, 54356 Illinois 41743, 36349, 44588, 40341, 32544, 38226, 46463, 42255, 38621, 32502, 37378, 40215, 41155, 38509, 47586, 46910, 56502, Massachusetts 48907, 41861, 51211, 55186, 39078, 48263, 48059,…
Two popular brands of tires for tractor-trailers are the Puma and the Eternal. Salma is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in the mean distance (in thousands of km) driven on them before they need to be replaced. In the company's testing lab, Salma tests a random sample of 14 Puma tires and a random sample of 15 Eternal tires. (These samples are chosen independently.) For the Puma tires, the sample mean distance (in thousands of km) until they would need to be replaced is 54.71 with a sample variance of 5.95. For the Eternal tires, the sample mean distance (in km) until they would need to be replaced is 50.21 with a sample variance of 37.75. Assume that the two populations of distances driven are approximately normally distributed. Can Salma conclude, at the 0.05 level of significance, that there is a difference between the population mean of the distances (in thousands of km) driven on Puma tires before…
An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 205 Fundash runners and 300 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 205 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.3 minutes. The 300 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.1 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, ,, of Fundash is not equal to the mean completion time, μ₂, of Coolsprint? Perform a two-tailed test.…
An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 250 Fundash runners and 285 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 250 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.7 minutes. The 285 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.6 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, u, of Fundash is not equal to the mean completion time, µa, of Coolsprint? Perform a two-tailed test.…
An amusement park keeps track of the percentage of individuals with season passes according to age category. An independent tourist company would like to show that this distribution of age category for individuals buying season passes is different from what the amusement park claims. The tourist company randomly sampled 200 individuals entering the park with a season pass and recorded the number of individuals within each age category. Age Category Child (under 13 years old) Teen (13 to 19 years old) Adult (20 to 55 years old) Senior (56 years old and over) Number of Individuals 56 86 44 14 The tourist company will use the data to test the amusement park’s claim, which is reflected in the following null hypothesis. H0:pchild=0.23H0:pchild=0.23, pteen=0.45pteen=0.45, padult=0.20padult=0.20, and psenior=0.12psenior=0.12. What inference procedure will the company use to investigate whether or not the distribution of age category for individuals with season passes is…
Phyllis, a college business student wants to study how many students in her class study for less than 20 hours per week. Past data reveals that the hours college students study per week has a mean of 29 with standard deviation 9 hours. The normal distribution for the population is shown by the dotted black line. She plans to take a random sample of 36 such college students and will calculate the mean hours studying to compare to the known hours studying. Compute the the mean and standard deviation of the sampling distribution of sample means for a sample of size 36. Round your answers to the nearest tenth. Show your answer by moving the two draggable points to build the sampling distribution.
Consider a random sample of 300 students in a university, 75 of them declared that they like playing football. Compute a point estimate of the proportion of all students who would like to play football.
A certain prescription medicine is supposed to contain an average of 250 parts per million (ppm) of a certain chemical. If the concentration is higher than this, the drug may cause harmful side effects; if it is lower, the drug may be ineffective. The manufacturer runs a check to see if the mean concentration in a large shipment conforms to the target level of 250 ppm or not. A simple random sample of 100 portions is tested, and the sample mean concentration is found to be 247 ppm. The sample concentration standard deviation is s = 12 ppm. What are the appropriate null and alternative hypotheses? Group of answer choices H 0: x̄ = 250 vs. H a: x̄ < 250 H 0: x̄ = 250 vs. H a: x̄ ≠ 250 H 0: x̄ = 250 vs. H a: x̄ > 250 H 0: μ = 250 vs. H a:μ < 250 H 0: μ = 250 vs. H a: μ ≠ 250 H 0: μ = 250 vs. H a: μ > 250
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Suppose that on a certain section of I-95, with a posted speed limit of 65 miles per hour, the speeds of all vehicles have a bell-shaped distribution with a mean of 72 mph and a standard deviation of 3 mph. Find the percentage of vehicles with the following speeds on this section of I-95: greater than 75 mph.
An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 240 Fundash runners and 200 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 240 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.2 minutes. The 200 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.4 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ1 , of Fundash is not equal to the mean completion time, μ2 , of Coolsprint?…

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS