(1) What are population mean, population variance, sample mean and sample variance? (2) Explain why sample...
(1) What are population mean, population variance, sample mean and sample variance?
(2) Explain why sample mean is a good approximation of population mean?
Homework Answers
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(1) What are population mean, population variance, sample mean
and sample variance?
(2) Explain why sample...
x, and S1 are the sample mean and sample variance from a population with mean μ|...
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
sample mean, sample s, variance, population s This data is from a sample. Calculate the mean,...
sample mean, sample s, variance, population s
This data is from a sample. Calculate the mean, standard deviation, and variance. x 42.6 23.9 12.9 22.8 41.3 26.1 | 13.6 14.4 44.3 Please show the following answers to 2 decimal places. Sample Mean = 26.88 Sample Standard Deviation = Sample Variance = (Please use the standard deviation above for your calcul Ooops - now you discover that the data was actually from a population! So now you must population standard deviation....
For the first population: sample mean is 17, sample variance is 1.5 and sample size is...
For the first population: sample mean is 17, sample variance is 1.5 and sample size is 14. The information for the second one is: sample mean is 19, sample variance is 1.8 and sample size is 16. What is the point estimate of the unknown common variance? A. 1.66 B. 0.46 C. 1.76 D. 3.30 E. 1.55
Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the...
Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the same variance σ. Let sỈ and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled is an unbiased estimator of σ2
4. Although the sample mean provides a good estimate of its population mean, sample variability tends...
4. Although the sample mean provides a good estimate of its population mean, sample variability tends to be biased. a. Explain what is meant by “biased.” b. How is sample variability biased? (Is it too large or too small?) c. How is this bias corrected in the formula for sample variance and sample standard deviation?
A random sample of 49 observations is used to estimate the population variance. The sample mean a...
A random sample of 49 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 59 and 3.1, respectively. Assume that the population is normally distributed. (You may find it useful to reference the appropriate table: chi-square table or F table) a. Construct the 90% interval estimate for the population variance. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval b. Construct the...
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
and 2. The variance of a sample depends a. the mean of the sample; the sample...
and 2. The variance of a sample depends a. the mean of the sample; the sample degrees of freedom b. the mean of the sample; the sum of squares for the sample c. the sum of squares for the sample; the sample degrees of freedom on 3. With an independent samples test, a researcher can draw conclusions about a. a comparison of two population means b. a comparison of two population variances c. the importance of sample size to the...
A random sample of n=7 observations are drawn from a normal population with mean and variance...
A random sample of n=7 observations are drawn from a normal population with mean and variance σ^2. The mean and variance of the sample are 1.45 and 2.07 respectively. Calculate a 90% confidence interval for the population standard deviation.
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
sample mean, sample s, variance, population s
This data is from a sample. Calculate the mean, standard deviation, and variance. x 42.6 23.9 12.9 22.8 41.3 26.1 | 13.6 14.4 44.3 Please show the following answers to 2 decimal places. Sample Mean = 26.88 Sample Standard Deviation = Sample Variance = (Please use the standard deviation above for your calcul Ooops - now you discover that the data was actually from a population! So now you must population standard deviation....
Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the same variance σ. Let sỈ and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled is an unbiased estimator of σ2
A random sample of 49 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 59 and 3.1, respectively. Assume that the population is normally distributed. (You may find it useful to reference the appropriate table: chi-square table or F table) a. Construct the 90% interval estimate for the population variance. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval b. Construct the...
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
and 2. The variance of a sample depends a. the mean of the sample; the sample degrees of freedom b. the mean of the sample; the sum of squares for the sample c. the sum of squares for the sample; the sample degrees of freedom on 3. With an independent samples test, a researcher can draw conclusions about a. a comparison of two population means b. a comparison of two population variances c. the importance of sample size to the...
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