Question

Suppose a particular brand of energy bars has come up with a new recipe. They want to know how many energy bars they need to test for calorie content in order to be 94% confident that the sample mean will be within 3 calories of the true mean

Answer 1

Complete Question

Suppose a particular brand of energy bars has come up with a new recipe. They want to know how many energy bars they need to test for calorie content in order to be 94% confident that the sample mean will be within 3 calories of the true mean? Suppose there is a population standard deviation of 20 calories

Answer:

The value is
`n =157`

Explanation:

From the question we are told that

The margin of error is
`E = 3`

The standard deviation is
`\sigma = 20`

From the question we are told the confidence level is 94% , hence the level of significance is

`\alpha = (100 - 94 ) \%`

=>
`\alpha = 0.06` \

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.881`

Generally the sample size is mathematically represented as

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

=>
`n = [\frac{1.881 } *  20 }{3} ] ^2`

=>
`n =157`