Can anyone explain blue writing step by step? A pollster believes that 20% of th

Question

Can anyone explain blue writing step by step?

A pollster believes that 20% of the voters in a certain area favor a bond issue. If 64 voters are randomly sampled from the large number of voters in this area, approximate the probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than06 Step-by-step solution Step 1 of 1 From the given information, consider a pollster believes that 20% of the voters in a certain area favor a bond issue. Consider the random sample of 64 voters from a large number of voters. The probability that the sample fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.06 Consider Ybe the number of voters a pollster believes. It follows binomial distribution where is this formula came from?ince I. The sample observations are independent. , 64 2. The probability of success is, p =0.2 3. The number of trials is finite Therefore, calculate the probability that the sample fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.06 as follows Isnt it supposed to be -p 0.06 0.06-P 7 Il -0.06 0.06 1 -0.06

Explanation / Answer

Please see below to find the answer is blue is not the right thing for the mentioned question:

Step 1:The formula you have written in blue is to get Z for the normal approximation to binomial distribution

We approximate mean and stdev using np and sqrt(npq)

Step 2: But if you want to use Z statistics for difference in proportions, then you can't use the above formula.

We normalize using the following:

Z = (p^ - p)/sqrt(p*p'/n),

where, p^ = Y/n, where Y and n are righly defined as in question

p^ - p is hypothesized to be test as difference of 0.06

Step 3: and the standard deviation is righly written as sqrt(p*p'/n)

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