according to the census, the median householde income in Atlanta (1.5 million ho
ID: 2957916 • Letter: A
Question
according to the census, the median householde income in Atlanta (1.5 million households) was $52000 IN 1999. iN JUNE 2003, A MARKET RESEARCH ORGANIZATIoN TAKES A SIMPLE RANDOM SAMPLE OF 750 HOUSEHOLDS IN aTLANTA; 56% OF THE SAMPLE households had incomes over $52000. Did median household income in Atlanta increase over the period 1999 to 2003?(a) Formulate null and alternative hypotheses in terms of a box model.
(b) Calculate the appropriate test statistic and P.
(c) Did the median family income go up?
Explanation / Answer
Since we are testing for proportion, a z-test is OK. Also, we have a large sample. a) H0: Median income in 2003 is $52,000 ( p=0.5) HA: Median income is over $52,000 (p > 0.5) p = proportion of people with income over $52,000 in 2003 b) Sample proportion phat = 0.56 Variance of proportion = p*(1-p)/n = 0.5(0.5)/750 =0.0003333 S.D. of p is sqrt[0.000333] = 0.0183 Z = ( 0.56 - 0.5 ) / 0.0183 = 3.2863 c) P( z > 3.29) = 0.00001 The critical z assuming a 5 % level of significance is 1.645. 3.29 > 1.645; hence, reject H0 and accept HA. The proportion of people with median income $52,000 is greater than 50 %. Note: We need to know in 1999, what percentage of people had income over $52,000 to precisely do a statistical test. (or at least a sample estimate taken in 1999).
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