MATH SOLVE

8 months ago

Q:
# A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been ________ and the probability of making an error would have been ________.

Accepted Solution

A:

Answer:narrower, reducedStep-by-step explanation:Given that a sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviationwe have confidence interval is margin of error on either side of mean.Margin of error= Critical value * std errorStd error in turn is inversely proportinal to square root of nFor same confidence level, if sample size is increased we get a less margin of error and hence a narrower confidence interval.when a confidence interval is narrowed, probability of making a type I error would be reduced.Hence we getIf a bigger sample had been used instead, then the 95% confidence interval would have been __narrower______ and the probability of making an error would have been ___reduced_____.