Answer :
Final answer:
To estimate the average weekly sales of the new footwear within $200 with 95% reliability, Fleet Shoes needs a sample size of at least 15 weeks of data.
Explanation:
To estimate the average weekly sales of the new footwear within $200 with a 95% reliability, we need to determine the sample size needed.
Using the formula:
n = (Z * σ) / E
Where:
n = sample size
Z = z-score for the desired level of confidence (in this case, 95%)
σ = standard deviation
E = margin of error (in this case, $200)
Plugging in the values, we get:
n = (1.96 * 1500) / 200 = 14.7 (approx.)
Rounding up, we need a sample size of at least 15 weeks of data.
Learn more about Sample Size Estimation here:
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Answer:
The number of weeks required = 216 weeks
Step-by-step explanation:
Given that:
Margin of Error E = 200
Confidence interval = 95% = 0.95
Level of SIgnificance = 1 - C.I
= 1 - 0.95
= 0.05
Standard deviation = 1500
The Critical value for Z :
[tex]Z_{\alpha/2} =Z_{0.05/2} \\ \\ = Z_{0.025} = 1.96[/tex]
The number of weeks( i.e the sample size (n) ) required is :
[tex]n = (\dfrac{Z_{\alpha/2} \times \sigma}{E})^2[/tex]
[tex]n = (\dfrac{1.96 \times 1500}{200})^2[/tex]
[tex]n = (14.7)^2[/tex]
n = 216.09
n ≅ 216 weeks