A planner in Shady, Texas suspects that there is a certain neighborhood

1. A planner in Shady, Texas suspects that there is a certain neighborhood, known as “Live Oak Grove,” where the average number of persons / household is statistically significantly smaller than that the national census data, which shows a population parameter: 2.61 persons / household. This neighborhood has attracted older single and couples without children. The planner wants to know if specifying smaller affordable homes for this neighborhood on a federal block-grant application would be appropriate. In a bit of a hurry as the grant application must be in the mail by the end of the week our planner decides to sample only 21 households in this neighborhood. The survey generates a sample mean = (2.3) persons / household, with a sample standard deviation of (.4) persons / household. Our planner decides on a 99% confidence level.

Calculate: 1) the critical value using a table; 2) the test value using the appropriate formula; then 3) state your decision to reject or fail to reject the Null; conclude by 4) describing the type and probability for committing an error due to sampling.