3) The heavy metal content in water is an important parameter to estimate. We wish to...
3) The heavy metal content in water is an important parameter to estimate. We wish to determine the average concentration of lead in the water of a river. A preliminary sample is used to estimate the variability. The preliminary sample of units indicates that the standard deviation is of 0.5 μg.
a) Note that first we must obtain the sample size that
guarantees a successful experiment. Determine the sample size
required to obtain an estimation error of the average of 0.11 μg
with 90% confidence.
b) Obtain the confidence interval for the standard deviation (with
98% confidence). Suppose that the standard deviation of a sample of
28 units is of 0.35 μg, and the standard deviation of the
population is of 0.38 μg.
c) Suppose that the standard deviation of a sample of 28 units is
of 0.35 μg and the standard deviation of the population is of 0.38
μg. Calculate the probability that the standard deviation of the
sample is less than 0.30 μg.
Homework Answers
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3) The heavy metal content in water is an important
parameter to estimate. We wish to...
It is desired to determine the average concentration of lead in the water of a river....
It is desired to determine the average concentration of lead in the water of a river. It uses a preliminary sample to estimate the variability. The preliminary sample indicates that the standard deviation is 0.4 Microg. a) To estimate the lead we must first obtain the sample size that guarantees that the experiment is successful. Determine the sample size required to obtain an error in the average estimate of 0.05 g with 90% confidence. b) Obtain the confidence interval for...
Consider a population having a standard deviation equal to 9.96. We wish to estimate the mean...
Consider a population having a standard deviation equal to 9.96. We wish to estimate the mean of this population. (a) How large a random sample is needed to construct a 95% confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.) The random sample is units. (b) Suppose that we now take a random sample of the size we have determined in part a. If we...
Is wanted to dermine the avarage concentration of the lead in the water of a river. Is used a pre...
Is wanted to dermine the avarage concentration of the lead in
the water of a river. Is used a preliminar sample to estimate de
variability.The preliminar sample indicates a standard deviation of
A)To estimate the lead first we need to obtain the size of the
sample to assure the experiment will be succesfull. Determine the
size required to obtain an error in the estimation of the avarage
of
with the 90% of trust.
B)Obtain the interval of trust for the...
we wish to estimate μ, the mean length of the fish in our pond. we take...
we wish to estimate μ, the mean length of the fish in our pond. we take a random sample of 65 fish and measure their lengths. for this sample, we find an average length of 4.53 cm, and a standard deviation of 0.8cm. i) using our observations as a pilot study, determine the sample size needed to estimate the mean μ within 0.1cm with 95% confidence. ii) find the upper confidence interval for μ
Suppose that we want to estimate the population average price μ for the grapes per pound....
Suppose that we want to estimate the population average price μ for the grapes per pound. Assume that the price per pound follows the normal distribution. (a). If for a random sample of grape prices obtained from 20 different stores, the sample average price X-bar = $ 1.33 with a sample standard deviation (price) s = $ 0.30 then construct a 95 % confidence interval for μ . (5 points) (b). If the average price obtained from 50 different stores...
QUESTION 21 If we change a 90% confidence interval estimate to a 99% confidence interval estimate...
QUESTION 21 If we change a 90% confidence interval estimate to a 99% confidence interval estimate while holding sample size constant, we can expect a. the width of the confidence interval to increase. b. the width of the confidence interval to decrease. c. the width of the confidence interval to remain the same. d. the sample size to increase. QUESTION 22 Which one of the following is a correct statement about the probability distribution of a t random variable? a....
4. Suppose a researcher, interested in obtaining an estimate of the average level of some enzyme...
4. Suppose a researcher, interested in obtaining an estimate of the average level of some enzyme in a certain human population, takes a sample of 36 individuals, determines the level of the enzyme in each, and computes a sample mean of 22. Suppose further it is known that the variable of interest is approximately normally distributed with a variance of 45. Give a 96% confidence interval of population mean 5. Suppose we find that, the average engine size in our...
Amanda Reaves , a zookeeper, wants to estimate the average weight gain of elephants who are...
Amanda Reaves , a zookeeper, wants to estimate the average weight gain of elephants who are on a new diet plan. A preliminary study found the standard deviation was estimated to be 5.50 kilograms. Determine the sample size that is required to estimate a population mean to within 0.95 kilograms with a 90% confidence interval.
1. A random sample of 82 customers, who visited a department store, spent an average of...
1. A random sample of 82 customers, who visited a department store, spent an average of $71 at this store. Suppose the standard deviation of expenditures at this store is O = $19. What is the e 98% confidence interval for the population mean? 2. A sample of 25 elements produced a mean of 123.4 and a standard deviation of 18.32 Assuming that the population has a normal distribution, what is the 90% confidence interval for the population mean? 3....
Determine the sample size needed to construct a 95% confidence interval to estimate the average GPA...
Determine the sample size needed to construct a 95% confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.2. Assume the standard deviation of the GPA for the student population is 25 The sample size needed is (Round up to the nearest integer.) Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion for the following sample proportions when the margin...
Consider a population having a standard deviation equal to 9.96. We wish to estimate the mean of this population. (a) How large a random sample is needed to construct a 95% confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.) The random sample is units. (b) Suppose that we now take a random sample of the size we have determined in part a. If we...
Is wanted to dermine the avarage concentration of the lead in
the water of a river. Is used a preliminar sample to estimate de
variability.The preliminar sample indicates a standard deviation of
A)To estimate the lead first we need to obtain the size of the
sample to assure the experiment will be succesfull. Determine the
size required to obtain an error in the estimation of the avarage
of
with the 90% of trust.
B)Obtain the interval of trust for the...
4. Suppose a researcher, interested in obtaining an estimate of the average level of some enzyme in a certain human population, takes a sample of 36 individuals, determines the level of the enzyme in each, and computes a sample mean of 22. Suppose further it is known that the variable of interest is approximately normally distributed with a variance of 45. Give a 96% confidence interval of population mean 5. Suppose we find that, the average engine size in our...
1. A random sample of 82 customers, who visited a department store, spent an average of $71 at this store. Suppose the standard deviation of expenditures at this store is O = $19. What is the e 98% confidence interval for the population mean? 2. A sample of 25 elements produced a mean of 123.4 and a standard deviation of 18.32 Assuming that the population has a normal distribution, what is the 90% confidence interval for the population mean? 3....
Determine the sample size needed to construct a 95% confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.2. Assume the standard deviation of the GPA for the student population is 25 The sample size needed is (Round up to the nearest integer.) Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion for the following sample proportions when the margin...
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