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Answer :
Final answer:
The company must sample at least 14 weeks of data to estimate the average weekly sales of the new footwear within $200 and with 95% reliability.
Explanation:
To estimate the average weekly sales of the new athletic footwear within $200 and with 95% reliability, we need to determine the sample size. The formula to calculate the sample size for a known standard deviation is:
n = (z * σ) / E
where:
n = sample size
z = z-score corresponding to the desired level of reliability (in this case, 95%, so z = 1.96)
σ = standard deviation
E = desired margin of error (in this case, $200)
Using the given information, we can substitute the values into the formula:
n = (1.96 * 1400) / 200
n ≈ 13.72
Since we cannot have a fractional sample size, we need to round up to the nearest whole number:
Therefore, the company must sample at least 14 weeks of data to estimate the average weekly sales of the new footwear within $200 and with 95% reliability.
Learn more about Sample Size Estimation here:
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Answer:
188 weeks of data must be sampled.
Step-by-step explanation:
From the information given, we can deduce that:
The Margin of error is within = 200
The confidence interval = 95%
The level of significance = 1 - C.I
= 1 - 0.95
= 0.05
The standard deviation = 1400
The number of weeks the data must be sampled can be determined by using the formula for sample size which is:
[tex]n =( \dfrac{Z_{\alpha/2} \times \sigma}{E} )^2[/tex]
[tex]n =( \dfrac{Z_{0.05/2} \times 1400}{200} )^2[/tex]
[tex]n =( \dfrac{1.96 \times 1400}{200} )^2[/tex]
[tex]n =( \dfrac{2744}{200} )^2[/tex]
[tex]n =( 13.72)^2[/tex]
n = 188.24
n ≅ 188
Thus, 188 weeks of data must be sampled.
