First time home buyers are an important segment of the ­housing market because this group allows current homeowners to sell their home and purchase another. In 2012, the median age of first time homebuyers was 31 years old. To find out if the housing market is improving, suppose the Federal ­Housing Administration would like to determine if the median age of first time buyers decreased in 2013. A random sample of first time buyers was collected and their ages were as follows.

Using α = 0.05, perform a hypothesis test to determine if the median age of first time buyers in 2013 was less than 31 years old.

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