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Two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, r and w. One confidence interval, i9, will be constructed using samples of size 9 from each of r and w, and the other confidence interval, i81, will be constructed using samples of size 81 from each of r and w. When all other things remain the same, which of the following describes the relationship between the two confidence intervals?

Sagot :

The option that describes the relationship between the two confidence intervals is; The width of I₈₁ will be¹/₉ the width of I₉

How to calculate width of the confidence interval with normal distribution?

The width of the confidence interval will be calculated from the formula;

W = 2Z(σ/√n)

where;

z is the z-score at given confidence level

σ is standard deviation

n is sample size

For first sample;

W_i9 = 2Z(σ/√9)

W_i9 =  ²/₃Zσ

For second Sample;

W_i81 = 2Z(σ/√81)

W_i81 = ²/₉Zσ

Thus, we will have;

W_i9/W_i81 = (²/₃Zσ)/(²/₉Zσ)

W_i9/W_i81 = 9

W_i81 = ¹/₉W_i9

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