Question

In: Statistics and Probability

3. (14) State whether each of the following is True or False. a. A smaller sample...

3. (14) State whether each of the following is True or False.

a. A smaller sample could provide less sampling error than a larger sample from a given population.

b. The correct critical value a lower tail hypothesis test when sigma is unknown, the sample size = 15, and alpha = 0.05 is -1.645.

c. A larger sample size can reduce the potential for extreme sampling error.

d. It is impossible for the population mean to equal the mean of a sample taken from it.

e. The size of sampling error depends on which sample is selected.

f. Sampling error is always caused by a biased sample.

g. The size of Type I error is determined by the researcher.

Solutions

Expert Solution

a) False. Sampling error decreases with the increase in sample size. It means, if there are small samples, then there is a high chance of sampling error & if there are large samples, then there is very low chance of sampling error.

b) False. We know that when sigma is unknown then to test the hypothesis, we calculate t-statistics with the degree of freedom is equal to (n-1). Thus, correct critical value a lower tail hypothesis test when sigma is unknown, the sample size = 15 is equal to the t-tabulated value for 14 degrees of freedom & 0.05 level of significance =-1.76

c) True. Since larger sample size can reduce the potential for extreme sampling error.

d) False. If you collect a random sample from the population, then there is a possibility that the sample mean is equal to the population mean because the sample mean is an unbiased estimator of the population mean. If you take the sample by another sampling technique, then there is less possibility that the sample mean is equal to the population mean.

e) False. Size of sampling error depends upon the sample size and also other factors like how to use your sample to estimate the population mean since there is more than one method to estimate single population parameter.

f) False. Sampling error does not always caused by a biased sample but it depends upon other factor also.

g) True. Size of type 1 error i.e. level of significance is always determined by the researcher like α=0.01 or α=0.05, extra.

orchestra answered 2 years ago
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