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Answer :
Final answer:
To estimate the average weekly sales of a new product line with a margin of error of $200 at a 90% confidence level, given a standard deviation of $1300, we can use the formula for sample size for proportions with these values to calculate the number of weeks of sales data needed.
Explanation:
The problem at hand revolves around calculating the size of the sample necessary to make a certain confidence interval prediction about the average weekly sales of a new footwear line. In this case, a 90% confidence is desired, meaning the probability that the sample results fall within the desired interval is 90%. In this context, it's also expressed that a margin of error of $200 is acceptable. Given that the initial sales indicate a standard deviation of $1300, we will use the sample size formula for proportions to calculate the number of data points necessary:
n = (Z2 * σ2) / E2
Where:
- Z is the z-score corresponding to the desired confidence level (1.645 for a 90% confidence interval),
- σ is the standard deviation of the population ($1300),
- E is the desired margin of error ($200).
Upon plugging in the given values we will be able to calculate the necessary number of weeks of data. Confidence interval estimations, standard deviations and sample size calculations play key roles in making these types of business decisions.
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