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Which Of The Following Is A Good Point Estimator For The Population Variance?

**S^2**

Which of the following is a good point estimator for the population variance?

S^2

For a quantitative variable in a particular population, how many different sample means are there?

Many

Which of the following is a good point estimator for the population standard deviation?

S

Which of the following is a good point estimator for the population mean?

x BAR

biased sample

A sample that does not fairly represent the population. A sample that overrepresents or underrepresents some segment(s) of the population

sampling frame

is a list which identifies all members of the population.

census

a count or measure of an entire population

sampling

a count or measure of part of a population and is more commonly used in statistical studies.

sampling error

the difference between the results of a sample and those of the population.

random sample

a sample that fairly represents a population because each member has an equal chance of inclusion

simple random sample

Every possible sample of the same size has the same chance of being selected

stratified sample

the population is divided into groups (strata) and a random sample is taken from each group (stratum)

cluster sample

Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters.

systematic sample

obtained by selecting every kth individual from the population. Choose a starting value at random. Then choose every kth member of the population.

convenience sample

Choose only members of the population that are easy to get.

Often leads to biased studies (not recommended).

Often leads to biased studies (not recommended).

sampling distribution of a statistic (such as the sample mean or sample proportion)

is the probability distribution of all values of the statistic when all possible samples of size n are taken from a population

point estimator

is a single-valued estimate calculated from the sample data, which is intended to be close to the true population value.

unbiased

If the average value of an estimator equals the population parameter being estimated, the estimator is said to be unbiased

standard error of the mean

is the standard deviation of a point estimator.

Central Limit Theorem

important theorem which summarizes the distribution of the sample mean. The distribution of the sample mean becomes closer to a normal distribution as the sample size becomes larger, regardless of the shape of the population for which the sample is drawn.

Which of the following is a good point estimator for the population variance?

Statistical inference uses statistics calculated from samples as the basis of an inference about the population. If the sample is representative, then the sample statistics (which are random variables that depend on which random sample is selected) ought to be close to their population counterparts. In other words, the sample mean ought to be close to the population mean, the sample proportion ought to be close to the population proportion, and the sample standard deviation should be close to the population standard deviation. Thus, a good point estimator for the population variance is s2.

Which of the following is a good point estimator for the population standard deviation?

Statistical inference uses statistics calculated from samples as the basis of an inference about the population. If the sample is representative, then the sample statistics (which are random variables that depend on which random sample is selected) ought to be close to their population counterparts. In other words, the sample mean ought to be close to the population mean, the sample proportion ought to be close to the population proportion, and the sample standard deviation should be close to the population standard deviation. Thus, a good point estimator for the population standard deviation is s.

For a quantitative variable in a particular population, how many different sample means are there?

The sample mean is the mean of a set of sample values taken from a population. Samples drawn from a population may vary in size and contain different data values. Thus, a quantitative variable in a particular population can have many different sets of sample values and there can be many sample means.

Which of the following is a good point estimator for the population mean?

Statistical inference uses statistics calculated from samples as the basis of an inference about the population. If the sample is representative, then the sample statistics (which are random variables that depend on which random sample is selected) ought to be close to their population counterparts. In other words, the sample mean ought to be close to the population mean, the sample proportion ought to be close to the population proportion, and the sample standard deviation should be close to the population standard deviation. Thus, a good point estimator for the population mean is x¯.

A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 93 months with a standard deviation of 9 months.

If the claim is true, what is the probability that the mean monitor life would be greater than 91.4 months in a sample of 66 monitors? Round your answer to four decimal places.

first, find the standard error

If the claim is true, what is the probability that the mean monitor life would be greater than 91.4 months in a sample of 66 monitors? Round your answer to four decimal places.

first, find the standard error

Assume the population from which the sample is drawn is extremely large. The distribution of x‾ would then be normal with μx‾=μ=93.

σ=Standard Deviation of the population=9

n=Sample Size=66

σx‾=√σ2/n= σ/√n = 9/√66 ≈ 1.107823

P(x‾>91.4)=P(x‾−μ/σx‾>91.4−93/1.107823) =P(z>91.4−93/1.107823)

≈P(z>−1.44)

Correct Answer:0.9251

σ=Standard Deviation of the population=9

n=Sample Size=66

σx‾=√σ2/n= σ/√n = 9/√66 ≈ 1.107823

P(x‾>91.4)=P(x‾−μ/σx‾>91.4−93/1.107823) =P(z>91.4−93/1.107823)

≈P(z>−1.44)

Correct Answer:0.9251

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 15 years with a variance of 25.

If the claim is true, in a sample of 41 wall clocks, what is the probability that the mean clock life would be greater than 15.4 years? Round your answer to four decimal places.

If the claim is true, in a sample of 41 wall clocks, what is the probability that the mean clock life would be greater than 15.4 years? Round your answer to four decimal places.

√25=5 5/√41≈0.7809

15.4-15=.4/0.7809

Correct Answer:0.3043

15.4-15=.4/0.7809

Correct Answer:0.3043

The mean per capita income is 18,904 dollars per annum with a standard deviation of 469 dollars per annum.

What is the probability that the sample mean would be less than 18850 dollars if a sample of 333 persons is randomly selected? Round your answer to four decimal places.

What is the probability that the sample mean would be less than 18850 dollars if a sample of 333 persons is randomly selected? Round your answer to four decimal places.

469/√333≈25.7010

18850-18,904=-54/25.7010

≈P(z<−2.10)

Correct Answer: 0.0178

18850-18,904=-54/25.7010

≈P(z<−2.10)

Correct Answer: 0.0178

A racing car consumes a mean of 86 gallons of gas per race with a standard deviation of 7 gallons.

If 41 racing cars are randomly selected, what is the probability that the sample mean would be greater than 84.1 gallons? Round your answer to four decimal places.

If 41 racing cars are randomly selected, what is the probability that the sample mean would be greater than 84.1 gallons? Round your answer to four decimal places.

7/√41≈1.0932

84.1-86/1.0932

≈P(z>−1.7380)

Correct Answer: 0.9589

84.1-86/1.0932

≈P(z>−1.7380)

Correct Answer: 0.9589

The mean weight of an adult is 76 kilograms with a variance of 100.

If 142 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 1.5 kilograms? Round your answer to four decimal places.

If 142 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 1.5 kilograms? Round your answer to four decimal places.

√100=10

10/√142≈0.8391813583

Since the true value of the population mean is 76, the value of x‾ should not fall between 74.5 and 77.5 in order for the error of estimation to be more than 1.5.

Correct Answer: 0.0739

10/√142≈0.8391813583

Since the true value of the population mean is 76, the value of x‾ should not fall between 74.5 and 77.5 in order for the error of estimation to be more than 1.5.

Correct Answer: 0.0739

The cost of 5 gallons of ice cream has a standard deviation of 7 dollars with a mean of 39 dollars during the summer.

What is the probability that the sample mean would differ from the true mean by more than 1.2 dollars if a sample of 188 5-gallon pails is randomly selected? Round your answer to four decimal places.

What is the probability that the sample mean would differ from the true mean by more than 1.2 dollars if a sample of 188 5-gallon pails is randomly selected? Round your answer to four decimal places.

7/√188=0.5105274702

Since the true value of the population mean is 39, the value of x‾ should not fall between 37.8 and 40.2 in order for the error of estimation to be more than 1.2 dollars.

Correct Answer: 0.0187

Since the true value of the population mean is 39, the value of x‾ should not fall between 37.8 and 40.2 in order for the error of estimation to be more than 1.2 dollars.

Correct Answer: 0.0187

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139mm, and a variance of 64.

If a random sample of 41 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2.1mm? Round your answer to four decimal places.

If a random sample of 41 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2.1mm? Round your answer to four decimal places.

√64=8

8/√141=1.249390095

Since the true value of the population mean is 139, the value of x‾ should not fall between 136.9 and 141.1 in order for the error of estimation to be more than 2.1mm.

Correct Answer: 0.0928

8/√141=1.249390095

Since the true value of the population mean is 139, the value of x‾ should not fall between 136.9 and 141.1 in order for the error of estimation to be more than 2.1mm.

Correct Answer: 0.0928

The mean life of a television set is 119 months with a standard deviation of 14 months.

If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months? Round your answer to four decimal places.

If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months? Round your answer to four decimal places.

14/√74=1.627466942

Since the true value of the population mean is 119, the value of x‾ should not fall between 117.9 and 120.1 in order for the error of estimation to be more than 1.1.

Correct Answer: 1.627466942

Since the true value of the population mean is 119, the value of x‾ should not fall between 117.9 and 120.1 in order for the error of estimation to be more than 1.1.

Correct Answer: 1.627466942

The quality control manager at a computer manufacturing company believes that the mean life of a computer is 120 months, with a standard deviation of 10 months.

If he is correct, what is the probability that the mean of a sample of 90 computers would be less than 117.13 months? Round your answer to four decimal places.

If he is correct, what is the probability that the mean of a sample of 90 computers would be less than 117.13 months? Round your answer to four decimal places.

10/√90=1.054092553

Correct Answer: 0.0032

Correct Answer: 0.0032

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 133 millimeters, and a standard deviation of 6 millimeters.

If a random sample of 43 steel bolts is selected, what is the probability that the sample mean would be greater than 132.4 millimeters? Round your answer to four decimal places.

If a random sample of 43 steel bolts is selected, what is the probability that the sample mean would be greater than 132.4 millimeters? Round your answer to four decimal places.

6/√43=0.914991422

Correct Answer: 0.7440

Correct Answer: 0.7440

Suppose the horses in a large stable have a mean weight of 1467lbs, and a standard deviation of 93lbs.

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable? Round your answer to four decimal places.

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable? Round your answer to four decimal places.

93/√49=13.28571429

Since the true value of the population mean is 1467, the value of x‾ must fall between 1458 and 1476 in order for the error of estimation to be less than 9.

Correct Answer: 0.5019

Since the true value of the population mean is 1467, the value of x‾ must fall between 1458 and 1476 in order for the error of estimation to be less than 9.

Correct Answer: 0.5019

The mean output of a certain type of amplifier is 287 watts with a standard deviation of 10 watts.

If 56 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.8 watts? Round your answer to four decimal places.

If 56 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.8 watts? Round your answer to four decimal places.

10/√56=1.33630621

Since the true value of the population mean is 287, the value of x‾ must fall between 285.2 and 288.8 in order for the error of estimation to be less than 1.8.

Correct Answer: 0.8220

Since the true value of the population mean is 287, the value of x‾ must fall between 285.2 and 288.8 in order for the error of estimation to be less than 1.8.

Correct Answer: 0.8220

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 28,631 miles, with a variance of 16,834,610.

What is the probability that the sample mean would differ from the population mean by less than 219 miles in a sample of 178 tires if the manager is correct? Round your answer to four decimal places.

What is the probability that the sample mean would differ from the population mean by less than 219 miles in a sample of 178 tires if the manager is correct? Round your answer to four decimal places.

√16,834,610=4103.000122

4103.000122/√178=307.5328611

Since the true value of the population mean is 28,631 miles, the value of x‾ must fall between 28412 and 28850 in order for the error of estimation to be less than 219.

Correct Answer: 0.5236

4103.000122/√178=307.5328611

Since the true value of the population mean is 28,631 miles, the value of x‾ must fall between 28412 and 28850 in order for the error of estimation to be less than 219.

Correct Answer: 0.5236

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