Question

A student makes a number of measurements of electrical current in the circuit. The average of the measurements is 12.33 mA. The standard deviation of the sample is 0.14 mA. How should this measurement be written to the correct number of significant figures with error range to show a 95% confidence

Answer 1

The way to represent this it is

`12.33 - (0.27)/(√(n) ) < \mu < 12.33 + (0.27)/(√(n) )`

Explanation:

From the question we are told that

The sample mean is

The standard deviation is

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

`\alpha = (100-95)`

`\alpha = 0.05`

The critical value for
`(\alpha )/(2)` is obtained from the normal distribution table that value is

`Z_{(\alpha )/(2) } = 1.96`

Now the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } * (s)/(√(n) )`

`E = (0.27)/(√(n) )`

Now the error range to show a 95% confidence is mathematically represented as

`\= x - E < \mu < \= x + E`

`12.33  -   (0.27)/(√(n) ) <  \mu < 12.33  +   (0.27)/(√(n) )`

Here notice that the significant figure is keep to three to match the significant figure of the given values