# Testing hypotheses of population mean

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A food processor is concerned that the 16 oz. can of sliced pineapple is being overfilled. The quality control department took a random sample of 50 cans and found that the arithmatic mean weight was 16.05 oz., with a sample standard deviation of .03 oz. At the 5% significance, can the hypothesis that the mean weight is equal to 16 oz. be rejected? Explain.

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The solution contains detailed explanations of testing whether the population mean is different from a given value.

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Solution. We can set up the null hypothesis: H0: u=16

<br> the alternative hypothesis H1: u is not 16.

<br>Denote the mean of sample by xbar and the sample standard deviation by SD. ...

###### Education

- 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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