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VARVARA [1.3K]
3 years ago
12

A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an a

ctual 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
Mathematics
1 answer:
storchak [24]3 years ago
7 0

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.

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