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 [tex]n =157 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 3[/tex]
The standard deviation is [tex]\sigma = 20[/tex]
From the question we are told the confidence level is 94% , hence the level of significance is
[tex]\alpha = (100 - 94 ) \%[/tex]
=> [tex]\alpha = 0.06[/tex] \
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.881[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
=> [tex]n = [\frac{1.881 } * 20 }{3} ] ^2[/tex]
=> [tex]n =157 [/tex]
