Estimating Total Sales at a Home Party

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SUMMARY

Janet sells cookware at home parties and aims to estimate the average spending per client. A random sample of 35 receipts yielded a mean (X̄) of $34.70 and a standard deviation (s) of $4.85. The 90% confidence interval for the average amount spent is calculated as 33.32 < X̄ < 36.09. Part (b) requires estimating the total sales for a party with 35 clients, which involves multiplying the average spending by the number of clients to derive a total sales range.

PREREQUISITES
  • Understanding of confidence intervals in statistics
  • Knowledge of basic statistical concepts such as mean and standard deviation
  • Ability to perform calculations involving sample sizes and averages
  • Familiarity with the concept of estimating totals from averages
NEXT STEPS
  • Learn how to calculate confidence intervals using different confidence levels
  • Explore the implications of sample size on statistical estimates
  • Study the relationship between averages and totals in statistical analysis
  • Investigate the use of statistical software for data analysis and confidence interval calculations
USEFUL FOR

Statisticians, data analysts, business owners estimating sales, and students studying statistics will benefit from this discussion.

ChrisBlack
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Homework Statement


Janet sells cookware at home parties, she wants to estimate the average amount a client spends at each party. A random sample of 35 receipts gave a mean of X bar = $34.70 with standard deviation s = %4.85.

a) find a 90% confidence interval for the average amount spent by all clients.

b) for a party with 35 clients, use part (a) to estimate a range of dollar values for Janet's total sales at that party.


Homework Equations





The Attempt at a Solution



I found the 90% confidence interval with no problem and got 33.32 < X bar < 36.09 but I don't understand what part (b) is asking, it seems to me that it is asking the same exact thing that (a) was
 
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ChrisBlack said:

Homework Statement


Janet sells cookware at home parties, she wants to estimate the average amount a client spends at each party. A random sample of 35 receipts gave a mean of X bar = $34.70 with standard deviation s = %4.85.

a) find a 90% confidence interval for the average amount spent by all clients.

b) for a party with 35 clients, use part (a) to estimate a range of dollar values for Janet's total sales at that party.


Homework Equations





The Attempt at a Solution



I found the 90% confidence interval with no problem and got 33.32 < X bar < 36.09 but I don't understand what part (b) is asking, it seems to me that it is asking the same exact thing that (a) was
(a) is asking about the average value, while (b) is asking for a total amount from 35 clients.
 

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