Question

The percentage of income spent on housing (including mortgage/rent, taxes, utilities) is an important factor loan agents use in approving customers for mortgages. A researched selected a sample of 20 homeowners in Florida and calculated their total housing costs are a percent of their monthly income. The researcher collected this information from the same 20 homeowners 5 years ago and again in 2019. The information collected is in the attached Excel data file. Is it reasonable to conclude the percent is less now than five years ago? Use a two-sample test of hypothesis to determine your answer. Explain and show your work, including the 6 steps for hypothesis testing.

Homeowner	Five Years Ago	Now
Holt	17	10
Pierse	20	39
Merenick	29	37
Lanoue	43	27
Fagan	36	12
Bobko	43	41
Kippert	45	24
San Roman	19	26
Kurimsky	49	28
Davison	49	26
Lozier	35	32
Cieslinski	16	32
Rowatti	23	21
Koppel	33	12
Rumsey	44	40
McGinnis	44	42
Pierce	28	22
Roll	29	19
Lang	39	35
Miller	22	12

Answer 1

Let be the mean housing cost before five years ago and let be the housing cost now.

The hypotheses will be

Used R. On RH.S. is output and on L.H.S. is code.

As p-value >  0.05. So, we will not reject the null hypothesis at 0.05 significance level and conclude that the housing cost is same as five years ago.