The minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.
The standard deviation is given as (σ) = 1.69.
The mean number of dresses given (μ) = 7.6.
Margin of error given (M.E.) = 0.14.
Confidence level given = 98%.
Z-Score corresponding to 98% confidence interval (Z) = 2.33.
We are asked to find the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval.
We assume the size of the sample to be n.
By the formula of Margin of Error:
M.E. = Z*(σ/√n).
Substituting the values, we get:
0.14 = 2.33*(1.69/√n),
or, √n = 2.33*1.69/0.14 = 28.126429,
or, n = 791.096 ≈ 791 (As sample size needs to be a whole number).
Thus, the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.
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