Please state whether the following statements are correct or incorrect. (24 pts.) _ 1. To carry out a study through a sample it is sufficient that The researcher is instructed to select the items when random. 2. The proportion of the universe included in the sample is a determining factor of the magnitude of the sampling error of the Estimate. 3. When the sample size is doubled, it happens that the interval The confidence of the estimate is reduced by half. 4. The purpose of a stratified sample is to reduce the dispersion by grouping the elements of the universe into classes that are more homogeneous than the universe as a whole. 5. The sample mean is an estimate of the population mean. 6. The statement that the proportion of the population is a point within 20 and.80, it is an example of a point estimate. _7. A confidence level of 95% corresponds to a coefficient z of 1.96. 8. An estimator is a rule that expresses how to calculate the estimate, based on sample information. 9. One of the advantages of point estimation is that it allows calculate the margin of error that is associated with the estimate 10. When the sample is considered small, the use of t distributions. eleven. The total margin of error is made up of the zort value and the error average standard. 12. An advantage of interval estimation is that it gives us ample is considered small, the use of t distributions. eleven. The total margin of error is made up of the zort value and the error average standard. _12. An advantage of interval estimation is that it gives us information about how close the estimate is with respect to the population parameter. Solve the following problems in light of the theory discussed in class. 1. A test is administered to five secretaries to determine the orthography. The results are presented below. Secretaries # of errors 3 B 8 2 D 11 E 6 to. Calculate the sample mean (10 pts.) b. Calculate the standard error of the mean (10 pts) Assume the following information: n = 25, p = -51, N = 400 to. Calculate the standard error of proportion (6 pts.) b. Construct a 95% confidence interval to estimate the (6 real proportion of the population. pts.) 6. Assume the following data n = 36, p= .48, N=800. to. Find the standard error of the proportion. (6 pts.) b. Construct a 99% confidence interval to estimate the real proportion of the population. (6 pts)