A simple random sample of 10 items resulted in a sample mean of 50, The populati

Question

A simple random sample of 10 items resulted in a sample mean of 50, The population standard deviation is = 20 a Compute the 95% confidence interval for the population mean. Round your answers to one decima place. Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.) b. Assume that the same sample mean was obtained from a sample of 90 items. Provide a 95% confidence interva for the population mean Round your answers o o decimal aces. c. What is the effect of a larger sample size on the interval estimate? - Select your answer- larger smaller Larger sample provides margin of error

Explanation / Answer

Mean is 50 and s is 20

z for 95% confidence is 1.96

a) this means that the upper bound is given by mean+s*z =50+20*1.96 =89.2

lower bound is given by mean-s*z =50-20*1.96 =10.8

b) standard error is given as s/sqrt(n) =20/sqrt(90)=2.1082

Thus upper bound is  mean+(standard error)*z =50+2.1082*1.96 =54.1321

Lower bound is mean-(standard error)*z = 50-2.1082*1.96=45.867928

c) larger sample size has reduced our confidence interval i.e made it smaller

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