A random sample of n = 36 observations has a mean x = 25.1 and a standard deviat

Question

A random sample of n = 36 observations has a mean x = 25.1 and a standard deviation s = 3.8. (a) Give the point estimate of the population mean 0.697 Find the 95% margin of error for your estimate. (Round your answer to four decimal places.) 1.241 (b) Find a 90% confidence interval for . (Round your answers to three decimal places.) 0.571 to 0823 what does "90% confident" mean? O There is a 90% chance that an individual sample mean will fall within the interval. 0 In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean. 90% of all values will fall within the interval limits. 0 In repeated sampling, 10% of all intervals constructed in this manner will enclose the population mean. There is a 10% chance that an individual sample mean will fall within the interval limits. (c) How many observations do you need to estimate to within 0.4, with probability equal to 0.95? (Round your answer up to the nearest whole number.) 347 observations

Explanation / Answer

Solution:- Given that n = 36 , X-bar = 25.1 , s = 3.8

a) the point estimate of the population mean = 25.1

b) 95% margin of error = Z * s/sqrt(n) = 1.96*3.8/sqrt(36) = 1.2413(round four decimal)

c) 90% confidence interval = X-bar +/- Z*s/sqrt(n)
= 25.1 +/- (1.645*3.8/sqrt(36))
= (24.058 , 26.142)

=> option A.

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