solve step by step and by your hand Note: please do not programm 8.5 The inspect

Question

solve step by step and by your hand
Note:
please do not programm

8.5 The inspection division of the Lee County Weights . and Measures Department is interested in estimatin actual amount of soft drink that is placed in 2- to at the local bottling plant of a large nationally tles known soft-drink company. The bottling plant has ision that the standard deviation for 2-liter bottles is 0.05 liter. A random sanm ple of 100 2-liter bottles obtained from this botting plant indicates a sample average of 1.99 liters Section 8 (a) Set up a 95% confidence interval estimate of the (b) Does the population of soft-drink fill have to be (c) Explain why an observed value of 2.02 liters is not true average amount of soft drink in each bottle. normally distributed here? Explain. 8. unusual, even though it is outside the confidence interval you calculated. uppose that the sample average had been 1.97 liters. What would be your answer to (a)? (d) S

Explanation / Answer

(a) Here population standard deviation = 0.05 litre

sample mean = x = 1.99 litre

95% confidence interval for true average amount of soft drink in each bottle= x +- Z95% ( / n)

= 1.99 +- 1.96 * (0.05/ 100)

= 1.99 +1.96 * 0.05/10

= (1.9802, 1.9998)

(b) No, to calculate cofidence interval for sample mean, the population doesn't need to be normal. As here n > 30 and we require sampling distribution of x, which is approximately normally distributed as per central limit theorem..

(c) Here an single value of 2.02 is not unusual as what we have calculated in part(a) is the confidence interval of true population mean when we repeatedly take samples of 100. Here taking one sample or one observation of 2.02 will not be unusual as this value is under the (2 +- 2 * 0.05)= (1.9, 2.1) level.

(d) Here if sample average is 1.97 litres.

the 95% confidence interval = 1.97 +- 1.96 * 0.05/10 = (1.9602, 1.9798)

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