Question

A) when creating a conference interval if we keep the level of confidence and the standard deviation constant then increasing the sample size will make the width of the interval

narrower or wider

B) when creating a conference interval if we keep the standard deviation and the sample size Constant then increasing the confidence will make the width of the interval

narrower or wider

C) when creating a confidence interval if we keep the level of confidence and the sample size constant then increasing the size of the standard deviation will make the width of the interval

narrower or wider

Answer 1

Confidence interval = +_ Z * ( / n)

is the sample mean

Z is the z-value which depends upon level of confidence

is standard deviation

n is sample size

Consider 1st Case here

when creating a conference interval if we keep the level of confidence and the standard deviation constant then increasing the sample size will make the width of the interval

Here Z is constant, is constant and sample size is increasing, since sample size is in the denominator, if it increased the Z * ( / n) value decreases, implying that the width of the interval will be narrower

Answer is narrower

Consider 2nd Case here

when creating a conference interval if we keep the standard deviation and the sample size Constant then increasing the confidence will make the width of the interval

Here n is constant, is constant and confidence is increasing, since as confidence increases Z increases, the Z * ( / n) value increases, implying that the width of the interval will be wider

Answer is wider

Consider 3rd Case here

when creating a confidence interval if we keep the level of confidence and the sample size constant then increasing the size of the standard deviation will make the width of the interval

Here n is constant, Z is constant and is increasing, since as increases, the Z * ( / n) value increases, implying that the width of the interval will be wider

Answer is wider