Estimating Total Sales at a Home Party

Using the confidence interval from (a), we can estimate a range of dollar values for Janet's total sales at a party with 35 clients. This would be calculated by taking the lower bound of the confidence interval and multiplying it by 35, and then taking the upper bound and multiplying it by 35. This gives us a range of $1166.20 to $1263.15 for Janet's total sales at a party with 35 clients. In summary, Janet wants to estimate the average amount a client spends at each party, and a random sample of 35 receipts gave a mean of $34.70 with a standard deviation of $4.85. To find a 90% confidence interval for the average amount spent,
  • #1
ChrisBlack
10
0

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
 
Physics news on Phys.org
  • #2
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.
 

What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence. It is used to estimate the population mean or proportion based on a sample of data.

How is a confidence interval calculated?

A confidence interval is calculated using the sample data, the desired level of confidence, and the standard error of the sample. The most common formula for calculating a confidence interval is: sample statistic ± (critical value x standard error)

What is the importance of a confidence interval?

A confidence interval provides a range of values within which we can be confident that the true population parameter lies. It helps us to understand the precision of our estimate and the amount of uncertainty associated with it.

What is the relationship between sample size and confidence interval?

The sample size and confidence interval have an inverse relationship. As the sample size increases, the confidence interval decreases, indicating a more precise estimate of the true population parameter. A larger sample size reduces the standard error, resulting in a narrower confidence interval.

How do confidence intervals differ from point estimates?

A confidence interval is a range of values, while a point estimate is a single value that represents the best guess of the population parameter. A confidence interval provides more information about the estimate, including its precision and uncertainty, while a point estimate provides only one value with no indication of its accuracy.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
662
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
4K
  • Precalculus Mathematics Homework Help
Replies
2
Views
5K
  • Calculus and Beyond Homework Help
Replies
1
Views
6K
  • Calculus and Beyond Homework Help
Replies
6
Views
3K
Back
Top