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A Food Marketing Institute found that 28% of households spend more than $125 a week on groceries. Assume the population proportion is 0.28 and a simple random sample of 372 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.29? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = ____

          A Food Marketing Institute found that 28% of households spend more than $125 a week on groceries. Assume the population proportion is 0.28 and a simple random sample of 372 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.29?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.
Answer = ____
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A Food Marketing Institute found that 28% of households spend more than $125 a week on groceries. Assume the population proportion is 0.28 and a simple random sample of 372 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.29? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = ____
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Transcript

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00:01 So this one's a binomial distribution where n is 426.
00:09 P is 0 .28 and 1 minus p is 0 .72.
00:17 The mean of the sampling distribution for p hat is p or 0 .28 because this is really p hat and 1 minus p hat and the standard deviation for the sampling distribution is the square root of p hat times 1 minus p hat p hat divided by n or the square root of 0 .28 times 0 .72 all divided by 426 which gives us a standard deviation of 0 .021754 remember z is always the data item minus the mean divided by the standard deviation and we want the probability that p hat is less than 0 .3 which is the same as the c being less than .3 minus .28 divided by our standard deviation...
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