Question

A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within 0.06 with 95% confidence

Answer 1

Answer:  267.

Step-by-step explanation:

When there is no prior information for the population proportion, then the formula we use to find the sample size to estimate the confidence interval :

$n=0.25(\dfrac{z^*}{E})^2$ , where z* = Critical z-value and E + amrgin of error.

Let p = proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label.

Since , we have no prior information about p. so we use above formula

with E = 0.06 and critical value for 95% confidence =z* =1.96  [By z-table ] , we get

$n=0.25(\dfrac{1.96}{0.06})^2=0.25(32.6666)^2\\\\=(0.25)(1067.111111)\\\\=266.777777778\approx267$

Hence, the required sample size is 267.