A researcher has a strange habit to use a sample size between √? and √?, where...

A researcher has a strange habit to use a sample size between √? and √?, where

? is the size of the population that she investigates. Under what circumstances, do you suggest her to use a correction factor for the variance of the sampling distribution while estimating a confidence interval for the population mean? What if she does not take your suggestion seriously? Describe the potential problems involved.

Solutions

Expert Solution

We should use a correction factor for the variance of the sampling distribution when more than 5% of the population is being sampled and the population has a known population size.

if she does not take your suggestion seriously (that is n > 0.05N) , then we sample a larger number of observations and the sample observations are not independent of each other . The Central Limit Theorem doesn’t hold and the variance of the estimate (e.g. the mean or proportion) will be too big. The potential problems involved would be high standard errors of the population mean and unreliable confidence interval estimates.

In this case, we nee to apply the correction factor as below.

The variance of the sampling distribution with finite population size and large sample size is,

where is the population standard deviation and n is the sample size.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A researcher has a strange habit to use a sample size between √? 3(Cube root of...

A researcher has a strange habit to use a sample size between √? 3(Cube root of N) and √? 2(Square root of N) , where ? is the size of the population that she investigates. Under what circumstances, do you suggest her to use a correction factor for the variance of the sampling distribution while estimating a confidence interval for the population mean? What if she does not take your suggestion seriously? Describe the potential problems involved.

A researcher has a strange habit to use a sample size between N^(1/3) and N^(1/2) ,...

A researcher has a strange habit to use a sample size between N^(1/3) and N^(1/2) , where N is the size of the population that she investigates. Under what circumstances, do you suggest her to use a correction factor for the variance of the sampling distribution while estimating a confidence interval for the population mean? What if she does not take your suggestion seriously? Describe the potential problems involved.

Continue to use same population and sample. Population Size of 150 with a sample size of...

Continue to use same population and sample. Population Size of 150 with a sample size of 49 Sample Mean is 519.04 Perform a hypothesis test of the claim that the true, but unknown population mean, is equal to 500, using a signicance level, = :02. 1. Using proper notation, write the correct null and alternative hypotheses. Indicate, which hypothesis is the claim, and state if the test is left-tailed, right-tailed, or 2-tailed. 2. Calculate the appropriate test statistic. 3. Use table...

A researcher estimated the following regression model with a sample size of 36. ?? = ?0...

A researcher estimated the following regression model with a sample size of 36. ?? = ?0 + ?1??1 + ?2??2 + ? The researcher wanted to find out whether there is heteroscedasticity in the error variance and so applied the White’s heteroscedasticity test. The result is as follows: ?? = −5.8417 + 2.5629??1 + 0.6918??2 − 0.4081??1 2 − 0.0491??2 2 + 0.0015??1??2 R 2 = 0.2143 What conclusion can you assist the researcher to draw at 5 percent and...

A researcher uses an ANOVA to compare nine treatment conditions with a sample size of n...

A researcher uses an ANOVA to compare nine treatment conditions with a sample size of n = 13 in each treatment. For this analysis find the degrees of freedom. What is df(treatment)? This is sometimes referred to as the “numerator degrees of freedom.” What is df(error)? This is sometimes referred to as the “denominator degrees of freedom.” If the scenario was changed so that there were still nine treatments, but there were different sample sizes for each treatment (a.k.a. an...

A researcher should use __________________ to analyze data when he has only a small sample, and...

A researcher should use __________________ to analyze data when he has only a small sample, and he knows that the sample was drawn from a population that is seriously skewed. inferential statistics. nonparametric statistics. parametric statistics. descriptive statistics. Which of these analytic techniques can be used to analyze data across three or more conditions of the IV? 1. t test 2. Analysis of variance 3. Chi-square 2 only 1 and 2 only 2 and 3 only 1, 2, and 3...

Suppose a sample has a sample mean of 53, a sample size of 40, and the...

Suppose a sample has a sample mean of 53, a sample size of 40, and the population has a standard deviation of 4. We want to calculate a 99% confidence interval for the population mean. The critical Z* in this case is 2.576. The confidence interval is (to one decimal place), a. (42.7, 63.3) b. (48.8, 57.2) c. (49, 57) d. (51.4, 54.6) e. (52.4, 53.6) f. (52.7, 53.3)

Discuss the issue of sample size in qualitative research. How might a qualitative researcher determine an...

Discuss the issue of sample size in qualitative research. How might a qualitative researcher determine an appropriate sample size? What influence does sample size have on transferability?

Sample A has a sample size of 12, a mean of 70, and a variance of...

Sample A has a sample size of 12, a mean of 70, and a variance of 160. Sample B has a sample size of 15, a mean of 75, and a variance of 180. Using a two-tail test with p < .05 significance, is there a difference between the means of the two samples? Group of answer choices Yes, Sample B has higher outcome scores than Sample A, t(25) = -0.987, p < .05. Yes, Sample B has higher outcome...

Describe the relationship between the width of a confidence interval and the size of the sample....

Describe the relationship between the width of a confidence interval and the size of the sample. Also describe the relationship between the width of the confidence interval and the degree of confidence. If a study yields an unsatisfactorily large confidence interval, what should be done? What prevents a researcher from continually increasing the sample size until a very small confidence interval is achieved?

Subjects