1. Closing costs for mortgages are an important concern for people buying homes. A realtor read an article in an industry publication that stated the mean closing costs for single-family homes in Michigan were $1958. She suspected that closing costs in her county were lower than that. To test this, the realtor took a random sample of 51 single-family home sales in her county. In the sample, the mean closing costs were $1822 and the standard deviation was $514. Perform a hypothesis test to determine whether the population mean closing costs in the realtor's county are lower than the mean in Michigan as a whole. Use an a = 0.05 significance level. Based on these results, can the realtor tell her clients that population mean closing costs are lower than $1958 in her county