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Consider a population with a mean ,1; : 206 and standard deviation 0' : 73. Suppose random samples of size n = 77 are selected from this population. 1. a) What is the mean of the distribution of the sample mean? Ha : l l b) What is the standard error of the mean? (2 decimal places) 0.34 l In the following questions, round the standard error and zscores to exactly 2 (two) decimal places before determining probabilities. Report probabilities accurate to at least 4 decimal places. 2. What is the probability that a randomly selected sample mean is: a) less than 213.7?l | b) greater than 201.6?| | c} less than 213.7 and greaterthan 201.6?| | d) less than 213.7 given greater than 201.6?l | e) less than 213.? or less than 201.6?l l I 3. Between what values would you expect to find the middle 86% of the sample means? Round to the nearest integer. Place the smaller value in the first box and the larger value in the second box. Between | and l 4. Why are we able to use the normal distribution in the calculations above? 0 Because the original population is normal 0 Becasuse the standard error is large enough -:i:- Because the sample size is large enough 0 Because the sample mean is large enough Question Help: I; Read El Video 8 Message instructor Submit Question - When constructing the confidence interval a population mean, assuming the population standard deviation is known, we use the following formula: Critical Value Standard Error Sample Mean _ 0' X i Za/Z Margin of Error v5 The table below contains information about two confidence intervals. Use the given information to determine the missing values: Round answers accurate to 2 decimal places. Confidence Level Interval 1 % Interval 2 97.00% Critical Value (351,92) 2.75 Sample Mean 106.80 Standard Error Margin of Error 31.90 5.80 Lower Limit 97,20 Upper Limit - In constructing a confidence interval for a population mean, which of the following are true? Select four (4) true statements from the list below: Note: A point is deducted 'For' each incor'r'ect selection. u - A confidence interval that fails to capture the population mean will also fail to capture the sample mean. , - if a confidence interval for the population mean is constructed from a sample of size n : 30, that interval must contain the population mean. , - lncreasing the sample size will reduce the width of the confidence interval. H - A 99% confidence interval must capture 99% of the population values. , - if the point estimate and lower limit for a confidence interval are 167.3 and 159.3 respectively, then the upper limit must be 175.3. _ - lncreasing the confidence level will not change the width of the confidence interval. H - The width of the confidence interval depends on the size of the sample mean. , - For the same sample data, a 95% confidence interval will be wider than a 99% confidence interval. C] - if a particular 93% confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the 89% confidence level. C] - A point estimate is a single population parameter that is used to estimate a sample statistic. C] - if a confidence interval does not contain the point estimate, then an error has been made in the calculation. C] - For a confidence level of 99%, the rightrtail area (1/2 : 0.005. Question Help: El Video 8 Message instructor Submit