Answer to Question #115465 in Statistics and Probability for YAN

Question

Q3. (Write down the measurement unit when applicable and correct your answers to 4 decimal places.)
A factory claims that the net weight of a bag of chips follows a Normal distribution with population standard deviation 1.5 grams, without disclosing the population mean weight. John is interested in knowing the population mean. He wants to estimate the population mean weight by himself. He buys 22 bags of chips and found that the total weight of 22 bags of chips is 1650 grams.
(a) Find a point estimate of the population mean weight of a bag of chips based on John’s information. (2 marks)
(b) Calculate the sampling error at 95% confidence. (5 marks)
(c) Construct a 95% confidence interval of the population mean weight of a bag of chips.

Answer 1

(a) $\bar x=\frac{1650}{22}=75\; g.$

(b) $SE=z_{0.025}\frac{\sigma}{\sqrt{n}}=1.96\frac{1.5}{\sqrt{22}}=0.6268\;g.$

(c) $95\%CI=(\bar x-SE, \bar x+SE)=(75-0.6268,75+0.6268)=(74.3732,75.6268).$