A real estate investment company is interested in the population proportion of new home sales that involved a VA loan. It is known that ten years ago in 2012, 15% of new homes sales involved a VA loan. We would like to assess if this proportion has increased (i.e. if the population proportion of new home sales in 2022 involving a VA loan is greater than 0.15). We will test at the 0.05 level of significance.

If we take a random sample of 78 home loans from this year and find that 16 of them used a VA loan, run an appropriate test of hypothesis, in particular: