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Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is
Step-by-step explanation:
From the question we are told that
The margin of error is
The confidence level is %
Given that the confidence level is 95% the level of significance is mathematically represented as
%
Next we obtain the critical value of from the normal distribution table , the values is
The reason we are obtaining critical values of
instead of
is because
represents the area under the normal curve where the confidence level interval (
) did not cover which include both the left and right tail while
is just the area of one tail which what we required to calculate the sample size
Now the sample size is mathematically represented as
substituting values
subtract 2y from both sides to get the y figures on the same side.
Then subract 3 from both sides to get the number values on the other side.
Divide by 2 to get y alone.