Question

. Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard deviation of flux container weight is determined to be 4 lb. How large a sample would be required to construct a 95% two-sided confidence interval on the mean that has a total width of 1 lb1 lb? (Montgomery, 08/2019, p. E-10) Montgomery, D. C. (2019). Introduction to Statistical Quality Control, Enhanced eText, 8th Edition. [[VitalSource Bookshelf version]]. Retrieved from vbk://9781119399308 Always check citation for accuracy before use.

Answer 1

The sample size is
`n  =  246`

Explanation:

From the question we are told that

The standard deviation is
`\sigma  =  4\ lb`

The confidence level is C = 95%

The total width is
`w = 1 \  lb`

Given that the confidence level is 95% then the level of significance is mathematically represented as

`\alpha = (100 -95 )\%`

=>
`\alpha = 0.05`

From the normal distribution table the critical value for
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.96`

Generally the sample size is mathematically represented as

`n  =  [\frac{Z_{(\alpha )/(2)}  * \sigma }{E}]^2`

Here E is the margin of error which is mathematically represented as

`E =  (w)/(2)`

=>
`E =  (1)/(2)`

=>
`E = 0.5`

So

`n  =  [(1.96 * 4 )/(0.5)]^2`

`n  =  246`