I now test was given to a simple random sample of 82 students at a certain college. The sample mean score was 105.6. Scores on this test are known to have a standard deviation =1. It is desired to construct 90% interval for the mean in scores of students at this college. What is the point estimated? The point estimate is Find the critical valve The critical valve is Find the standard error. Round to four decimal places The standard error is Find the margin of error. Round to two decimal places. The margin of error is Construct the 90% confidence interval. Rounds to one decimal place. The confidence interval are Is it likely that the population mean u is greater than 100? Yes or no it is or is not likely that the population mean u is greater than 100

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...