Asample 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

narrower, reduced

Step-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 deviation

we have confidence interval is margin of error on either side of mean.

Margin of error= Critical value * std error

Std error in turn is inversely proportinal to square root of n

For 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 get

If 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.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

think the answer would beb