1. A statistician wants to study the mean income per year for teachers in Mansoura city. Assume there are 100 households in the rural I, 50 in the rural II, 120 in the rural III, and 130 in the rural IV. The statistician decides to select 32 households from the rural I, 12 households from the rural II, 36 households from the rural II, and 70 from the rural IV where the (mean, standard deviation) for each rural are (15.13,8.61), (40.54, 4.68), (29.35, 6.57), (18.75, 6.57), respectively. a. Why or why not it makes sense to use a stratified random sample for this problem? b. Estimate the overall mean and variance of the estimator of mean. Also estimate the total and the variance of the estimator of total with a 95% confidence intervals for each of them. (t = 2.08). c. Do you think that the aims of the stratified random sample are satisfied? 2. Define the sample proportion of Y, and prove that the variance of the sample proportion is an unbiased estimator population proportion.

1. A statistician wants to study the mean income per year for teachers in Mansoura city. Assume there are 100 households in the rural I, 50 in the rural II, 120 in the rural III, and 130 in the rural IV. The statistician decides to select 32 households from the rural I, 12 households from the rural II, 36 households from the rural II, and 70 from the rural IV where the (mean, standard deviation) for each rural are (15.13,8.61), (40.54, 4.68), (29.35, 6.57), (18.75, 6.57), respectively. a. Why or why not it makes sense to use a stratified random sample for this problem? b. Estimate the overall mean and variance of the estimator of mean. Also estimate the total and the variance of the estimator of total with a 95% confidence intervals for each of them. (t = 2.08). c. Do you think that the aims of the stratified random sample are satisfied? 2. Define the sample proportion of Y, and prove that the variance of the sample proportion is an unbiased estimator population proportion.

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

Related questions

Q: Suppose that the quarterly sales levels among the health care information systems companies are…

A: Given that the mean of 8 million dollars and a standard deviation of 1.2 million dollars. μ=8σ=1.2…

Q: One year Thomas had the lowest ERA (earned-run average, mean number of runs yielded per nine…

A: We have given that X~N( μ , ?^2 ) Z-score =( x - μ )/?

Q: The MP3 player, aPod, made by Mango Corp., has an average battery of 400 hours. Battery life for the…

Q: A 4 year college will accept any student ranked in the top 60% of a national exam. If the test…

A: From the given information,Mean (µ) =600Standard deviation (σ) = 100Let the test score be a x which…

Q: Suppose the mean height in inches of all 9th grade students at one high school is estimated. The…

A: Given that Sample size n =9 Population standard deviation =3

Q: 2. A study reported in The Journal of Consumer Research dealt with the influence of touch on…

A: Given that,Females diners who were touched:The sample size is 35.The sample mean is 3.84.The…

Q: 2. A manufacturer does not know the mean and standard deviation of the diameters for the production…

A: Let μ be the mean and σ be the standard deviation of the diameters of the ball bearings. The…

Q: A company that manufactures and bottles apple juice uses a machine that automatically fills 16-ounce…

A: The amount normally distributed μ=16σ=1

Q: Suppose an anthropologist discovered a new African tribe consisting of 356 people. He measured the…

A: We use the code below to calculate the above:

Q: The National Center for Health Statistics reports that the average systolic blood pressure for males…

A: Here, The claim to be tested is "The medical director of a large company believes the average…

Q: Suppose 18% of movie-goers say that horror is their favorite movie genre. If a random sample of…

A: Obtain the mean number of movie-goers that prefer horror movie genre. The mean number of movie-goers…

Q: The Queen decided to change the distribution of wealth in Arecima. With the help of the royal…

A: Given Information: The mean was increased from 100 to 120. The standard deviation was reduced from…

Q: STEP ONE: STEP TWO: STEP THREE: STEP FOUR: STEP FIVE: STEP SIX: Test Statistic: Critical Value(s):

A: n1 = 123 n2 = 290 x1 = 0.83 x2 =1.39 s1 = 1.77s2 =3.06

Q: A population of Senior High School consits of number 1,2,3,4 and 5 .Compute the mean ,variance and…

Q: 5. The following are raw marks of 8 students in a Satatistics assessment. 36, 50, 17, 22, 25, 20,…

Q: For each day of last year, the number of vehicles passing through a certain intersection was…

Q: Suppose that the quarterly sales levels among health care information systems companies are…

Q: At Center Hospital there is some concern about the high turnover of nurses. A survey was done to…

A: Given data for 20 nurses were as follows. 5, 8, 10, 11, 11, 14, 15, 17, 23, 26, 26, 28, 29, 30, 31,…

Q: Determine the sales level (in millions of dollars) that is the cutoff between quarters that are…

A: Suppose that the quarterly sales levels among health care information systems companies are…

Q: At Center Hospital there is some concern about the high turnover of nurses. A survey was done to…

A: Data:3, 6, 8, 9, 9 12, 13, 15, 21, 24, 24, 26, 27, 28, 29, 30, 32, 37, 37, 43 Using online…

Q: 3) A sample of 10 students scored the following grades: 15, 19, 17, 39, 33, 20, 18, 37, 31, 35.…

A: 3) i) To find the median we arrange the data first 15 17 18 19 20 31 33 35 37 39…

Q: 5. An industrial machine manufactures beams for sale whose length follows a normal distribution with…

Q: An airline company wants to estimate the mean number of unoccupied seats per flight over the past…

A: Given : Sample Size (n) = 225 Sample Mean (X¯) = 8.5 Sample SD (S) = 5.4 Confidence Level = 90% So ;…

Q: researcher asks six (6) families how many times they ordered delivery from Amazon in the last six…

A: The given values are 6, 9, 2, 12, 6, and 5. It will consider as a population. The population size is…

Q: uppose that the quarterly sales levels among health care information systems companies are…

A: Suppose that the quarterly sales levels among health care information systems companies are…

Q: 3(a). Develop hypotheses that can be used to determine whether mean annual Medicare spending in…

A: Given that ; μ = $ 6883 n = 49 Sample mean = $ 5978.32 s = $ 2513 By using this information we…

Q: ) H0: ?1 − ?2 = 0 Ha: ?1 − ?2 > 0 t=_________ P-value_______ State the conclusion in the…

Q: Consider the asSsessment that you administered to your 23 third-graders last week. The scores…

A: To calculate the mean deviation MDD and standard deviation σD of the given data: Mean deviation is…

Q: A government board examination has a mean score of 500 points. A review school promises improved…

A: Let μ denotes the population mean score. The government board examination has a mean score of 500…

Q: (a) What percentage of the population lives in affluence? (b) An amended tax law is expected to…

A: Let X be the random variable that family income. Given that, X ~ N(μ = 40,000, σ=12,000) The minimum…

Q: Suppose a small paint manufacturing company has a daily production that is normally distributed with…

Q: The total blood cholesterol levels in a certain Mediterranean population are found to be normally…

A: We have to find given probability

Q: Suppose that the quarterly sales levels among health care information systems companies are…

Q: 3. The average ULP pump price (in cents per Litre) in South Australia for each year since 2015 is:…

A: Average is the sum of all terms divided by number of terms

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

1. A statistician wants to study the mean income per year for teachers in Mansoura city.
Assume there are 100 households in the rural I, 50 in the rural II, 120 in the rural III, and
130 in the rural IV. The statistician decides to select 32 households from the rural I, 12
households from the rural II, 36 households from the rural III, and 70 from the rural IV
where the (mean, standard deviation) for each rural are (15.13,8.61), (40.54, 4.68),
(29.35, 6.57), (18.75, 6.57), respectively.
a. Why or why not it makes sense to use a stratified random sample for this problem?
b. Estimate the overall mean and variance of the estimator of mean. Also estimate the total
and the variance of the estimator of total with a 95% confidence intervals for each of them.
(t = 2.08).
c. Do you think that the aims of the stratified random sample are satisfied?
2. Define the sample proportion of Y, and prove that the variance of the sample proportion is
an unbiased estimator population proportion.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Benjamin owns a small Internet business. Besides himself, he employs nine other people. The salaries earned by the employees are given next in thousands of dollars (Benjamin’s salary is the largest, of course): 30, 30, 45, 50, 50, 50, 55, 55, 60, 75 Determine the range, population variance, and population standard deviation for the data.
A quality control engineer at Shell visits 80 gas stations and collects a fuel sample from each. She measures the sulphur content in the gas and sorts the samples into 4 different batches. She finds: 19 samples with less than 180 ppm sulphur, 20 samples with between 180 and 230 ppm, 23 samples with between 230 and 280 ppm, and 18 samples with more than 280 ppm. Does the sulphur content of gas follow a normal distribution with a mean of 230 ppm and a standard deviation of 50 ppm at the 5% significance level
The average amount of rainfall in Puerto Rico last month was 3.5 inches, according to the National Meteorology Center. Suppose that a normal distribution can be used and that the standard deviation is 0.8 inches. a. What percentage of the time was last month's rainfall greater than 4 inches? (3 points)b. What percentage of the time was rainfall less than 3 inches? (3 points)c. A month is considered extremely humid if the rainfall is 10% higher for that month. How much rainfall must be in April to be considered an extremely humid month? (3 points)
Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 12 million dollars and a standard deviation of 1.3 million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 20% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. million dollars X S
1. If X - N(200,2²), find а) Р(X < 197) b) Р(X < 200.5) 2. Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a. greater than 69 c. greater than 101 b. less than 73 d. less than 87 3. Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 29 and 36 b. between 22 and 35 4. Let X denote the time taken to run a road race. X is normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. in less than 160 minutes? b. in 215 to 245 minutes?
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 260 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. -Find the 70th percentile of the distribution of the average of 49 fly balls
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 the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 9 million dollars and a standard deviation of 1.4 million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 10% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
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.
Suppose the midterm exam score for 100 students at UPC had a mean of 70 and a standard deviation of 5. How many students scored between 55 and 85 marks 65 and 75 marks
Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 8vmillion dollars and a standard deviation of 1.1million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 15%of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
Imagine that for those who meditate daily, the number of minutes in meditation has mean 35 and standard deviation 10. In a group of 200 such persons, how many are expected to meditate more than 43 minutes per day?