Question 1076466
sample size = 1000


459 of those 1000 found their real estate agent through a friend.


alpha = .08


claim is that 46% of home buyers find their real estate agent through a friend.


46% is equal to .46.


your null hypothesis is that the probability that prospective home buyers find their real estate agent through a friend is .46


your alternate hypothesis is that the probability that prospective h ome buyers find their real estate agent through a friend is something different than .46


this indicates a two tailed alpha since the claim is that the real percent could be more than or less than 46%.


since alpha is .08, then you would divide it by 2 to get alpha/2 = .04


the critical z-score for an alpha of .04 would be found by looking in the z-score table or using a z-score calculator to find a z-score that has an area of .96 to the left of it.


i used the z-score calculator by statrek to find that the critical z-score would be plus or minus 1.751 which i then rounded to 1.75.


using my ti-84 plus calculator, the critical z-score was found to be plus or minus 1.750686071.


you may round as your instructor requires.


my answer is based on the critical z-score of plus or minus 1.75.


your sample p is equal to .459


your sample q is equal to 1 - p which makes it equal to .541.


your sample standard error is equal to sqrt((p*q/n) = sqrt(.459*.541/1000) which is equal to .01567581408 which i rounded to .0156758.


your sample z-score would be equal to (x-m)/s which translates to (.459 - .46) / .0156758 which is equal to -.0637925975 which i rounded to -.06.


your sample z-score of -.06 is less than your critical z-score of -1.75.


this indicates that the probability of a difference between your sample mean and the state mean is due largely to chance variations in sample means of samples with a sample size of 1000.


you therefore can't reject the null hypothesis.


that's my take on this problem based on the information you provided.


a reference for determining the mean and standard error of a proportion can be found here:


<a href = "http://onlinestatbook.com/2/sampling_distributions/samp_dist_p.html" target = "_blank">http://onlinestatbook.com/2/sampling_distributions/samp_dist_p.html</a>