At a local high school with over 2,000 students, 65% of the student body participates in a schoolsponsored extracurricular activity. Suppose that the school newspaper is doing an article on studentparticipation in extracurricular activities and surveys a random sample of 100 students about theirparticipation. Let p represent the proportion of students who participate in an extracurricular activityin a sample of size 100. Why is the sampling distribution of p approximately normal?(A) Because np and n(1 - p) are both sufficiently large.(B) Because the sample was randomly selected.(C) Because the sample size is less than 10% of the population size.(D) Because the sampling distribution of a sample proportion is always approximately normal.(E) The sampling distribution of p is not approximately normal because the survey question has onlytwo possible answers, and a binary variable cannot be approximately normally distributed.

The sampling distribution of a statistic is the distribution of that statistic, considered as a…

Answered: At a local high school with over 2,000…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider two populations for which μ₁ = 34,0₁ = 3₁ μ₂ = 27, and σ₂ = 4. Suppose that two independent random samples of sizes n₁ = 47 and n₂ = 54 are selected. Describe the approximate sampling distribution of x₁ - x₂ (center, variability, and shape). What is the shape of the distribution? O The distribution would be non-normal. O The distribution is approximately normal. O The shape cannot be determined. What is the mean of the distribution? What is the standard deviation of the distribution? (Round your answer to three decimal places.)
A random sample of communities in western Kansas gave the following information for people under 25 years of age.
An exclusive school in Manila made a study on the relationship of age and teaching performance of teachers as evaluated by the students using the 5-point scale, where 5 is the highest. With a random sample of 16 teachers, test if the relationship is significant using the 0.05 level. The result of the sampling is shown below: Teacher No. 1234 3456NHO 60095 7 8 10 11 12 13 14 15 16 Age (x) 38 30 37 42 45 528 mo 52 48 33 36 32 950 49 48 56 30 44 43 Performance (y) 3.89 4.12 4.05 3.61 3.08 2.58 3.42 4.47 4.68 4.39 2.96 3.01 2.80 4.34 3.67 3.55
Suppose a simple random sample of size n= 125 is obtained from a population whose size is N= 25,000 and whose population proportion with a specified characteristic is p= 0.8. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because ns0.05N and np(1- p) 2 10. O B. Approximately normal because ns0.05N and np(1- p) 2 10. O C. Not normal because ns0.05N and np(1- p) < 10. O D. Approximately normal because ns0.05N and np(1- p) < 10. Determine the mean of the sampling distribution of p. Ha = (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. OA = (Round to six decimal places as needed.) (b) What is the probability of obtaining x= 105 or more individuals with the characteristic? That is, what is P(p 20.84)? P(p20.84) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x =…
In 2006, 12.5% of all live births in the United States were to mothers under 20 years of age. A sociologist claims that births to mothers under 20 years of age is decreasing. The sociologist conducts a simple random sample of 46 births and finds that 6 of them were to mothers under 20 years of age. Test the sociologist's claim at the level of significance. Preliminary: a. Is it safe to assume that n < 5% of all mothers under 20 years of age in the United States? No Yes b. Verify np(1 - p) ≥ 10. Round your answer to one decimal place. np(1 - p) = 5.0 c. Since np(1 - p) < 10, we should use which distribution to obtain the p-value? exponential distribution uniform distribution binomial distribution Note: Without being given that the population is normally distributed, and that np(1 − p) < 10, we cannot assume normal distribution and are required to use the binomial distribution. Test the claim: a. What are the null and alternative hypotheses? Hop H1: p 0.125 0.125 b. Based on the…
The acceptable level for insect filth in a certain food item is 2 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x= 2.6 insect fragments per ten-gram portion. Complete parts (a) through (c) below. (a) Why is the sampling distribution of x approximately normal? O A. The sampling distribution of x is approximately normal because the population is normally distributed. O B. The sampling distribution of x is assumed to be approximately normal. OC. The sampling distribution of x is approximately normal because the sample size is large enough. O D. The sampling distribution of x is approximately normal because the population is normally distributed and the sample size is large enough. Click to select your answer and then click Check Answer. 5 parts remaining Clear All Chect Arw P Type here to search AD4 4 ENG 746 PM 3/28/2021 DELL 1Home PoUp Delete PrtScr Insert…
Suppose a simple random sample of size n= 125 is obtained from a population whose size is N = 20,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1- p) 2 10. O B. Approximately normal because ns0.05N and np(1- p) < 10. O C. Not normal because ns0.05N and np(1- p) 2 10. O D. Not normal because ns0.05N and np(1 - p)< 10. Determine the mean of the sampling distribution of p. = (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. =(Round to six decimal places as needed.) (b) What is the probability of obtaining x= 55 or more individuals with the characteristic? That is, what is P(p20.44)? P(p20.44) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 40 or…
Suppose a simple random sample of size na 150 is obtained from a population whose size is N 25,000 and whose population proportion with a specifed characteristic is p=0.6. Complete parts (a) through (c) below, (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below QA Not normal because ns0.05N and np(1-p) 10. OB Approximately normal becausens0.05N and np(1-p)< 10. OC. Not nomal because ns0.05N and np(1- p) 1o. o. Approximalely nomal becausens0.0SN and ne(t-pa 10 Determine the mean of the sampling distribuion of p H Round to one decimal place as needed)
An article reported that in a large study carried out in the state of New York, approximately 60% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that p 0.6. (a) Would p based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not. Yes, because np 10 and n(1 − p) > 10. No, because np 10. (b) What are the mean value and standard deviation of p based on a random sample of size 390? (Round your standard deviation to four decimal places.) mean standard deviation (c) When n = 390, what is P(0.55 ≤ ≤ 0.65)? (d) Is the probability calculated in Part (c) larger or smaller than would be the case if n = 490? Answer without actually calculating this probability. The probability from Part (c) is larger because as n increases, the standard deviation of increases. The probability from Part (c) is larger because as n…
Suppose a simple random sample of size n= 50 is obtained from a population whose size is N= 10,000 and whose population proportion with a specified characteristic is p= 0.4. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because n 10. C. Approximately normal because ns0.05N and np(1 - p) < 10. O D. Not normal because n <0.05N and np(1 - p) 2 10. Determine the mean of the sampling distribution of p. HA = (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. On = (Round to six decimal places as needed.) (b) What is the probability of obtaining x= 21 or more individuals with the characteristic? That is, what is P(p 2 0.42)? P(p 20.42) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 16 or fewer individuals with the characteristic? That is, what is P(ps0.32)?…
Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds): 3.06 4.97 5.01 4.13 5.02 2.91 3.88 2.55 2.91 5.18 3.68 4.54 2.65 4.14 5.11 3.19 Use a calculator to verify that the sample variance for this plot is s^2=0.923. Another random sample of years for a second plot gave the following annual wheat production (in pounds): 3.61 3.50 3.81 3.89 3.84 3.50 3.53 3.62 3.67 4.05 3.82 4.12 3.75 3.92 4.05 4.01 Use a calculator to verify that the sample variance for this plot is s^2=0.042. Suppose that we test the claim using a=0.01 that the population variance of annual wheat production for the…
Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 20,000 and whose population proportion with a specified characteristic isp=D0.2. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1 - p)< 10. O B. Not normal becausens0.05N and np(1- p)< 10. O C. Not normal because ns0.05N and np(1-p)2 10. OD. Approximately normal because ns0.05N and np(1 - p) 2 10. Determine the mean of the sampling distribution of p. HA = 0.2 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. GA = (Round to six decimal places as needed.)

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