Asked by Natasha Finkelstein on Jul 05, 2024
Verified
A random sample of 100,000 credit sales in a department store showed an average sale of $87.25.From past data, it is known that the standard deviation of the population is $20.00.What is the 95% confidence interval of the population mean?
A) $87.22 to $87.28
B) $87.13 to $87.37
C) $19.97 to $20.03
D) $19.88 to $20.12
Confidence Interval
A range of values, derived from sample statistics, that is believed, with a certain level of confidence, to contain the population parameter of interest.
Credit Sales
Sales made by a business for which payment will be made at a later date, as opposed to immediate cash sales.
- Acquire knowledge on how to calculate the standard error and its relevance when dealing with population means.
- Gain insight into the roles of sample size and confidence levels in affecting the margin of error and the calculation of confidence intervals for population means and proportions.
Verified Answer
PC
Pamela CrenshawJul 11, 2024
Final Answer :
B
Explanation :
To find the 95% confidence interval for the population mean, we can use the formula:
CI = X̄ ± z* (σ/√n)
where X̄ is the sample mean, σ is the population standard deviation, n is the sample size, and z* is the z-score for the desired level of confidence.
For a 95% confidence interval, z* = 1.96.
Substituting the given values, we get:
CI = 87.25 ± 1.96 * (20/√100,000)
CI = 87.25 ± 0.12
CI = (87.13, 87.37)
Therefore, the best choice is B, which is the interval (87.13, 87.37), since this is the only option that includes the correct confidence interval for the population mean.
CI = X̄ ± z* (σ/√n)
where X̄ is the sample mean, σ is the population standard deviation, n is the sample size, and z* is the z-score for the desired level of confidence.
For a 95% confidence interval, z* = 1.96.
Substituting the given values, we get:
CI = 87.25 ± 1.96 * (20/√100,000)
CI = 87.25 ± 0.12
CI = (87.13, 87.37)
Therefore, the best choice is B, which is the interval (87.13, 87.37), since this is the only option that includes the correct confidence interval for the population mean.
Learning Objectives
- Acquire knowledge on how to calculate the standard error and its relevance when dealing with population means.
- Gain insight into the roles of sample size and confidence levels in affecting the margin of error and the calculation of confidence intervals for population means and proportions.