# Finding the Minimum Sample Size

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The branch manager of a pet supply store wants to study characteristics of customers of his store. In particular, he decides to focus on two variables: the amount of money spent by customers and whether the customers own only one cat.

1. If he wants to have 95% confidence of estimating the true population mean amount spent in his store within ± $1.50 and the standard deviation is assumed to be $10, what sample size is needed with calculations?

2. If he wants to have 90% confidence of estimating the population proportion of customers who own only a cat to within ± 0.045, what sample size is needed with calculations?

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The solution consists of details of how to find out the minimum sample size.

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1. If he wants to have 95% confidence of estimating the true population mean amount spent in his store within ± $1.50 and the standard deviation is assumed to be $10, what sample size is needed with calculations?

Solution. Assume that the standard ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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