You conduct a study in a large southern town to determine whether the average amount spent on food per four-person family in the town is lower than the national average per four-person family.A random sample of the weekly grocery bills of 50 four-person families reveals a mean of $145.88 and a standard deviation of $17.2988616.Usingexactlythese numbers and an alpha level of .05, and producing accurate calculations:

1. What is the null hypothesis (in words)?
2. What is the alternative hypothesis (in words)?
3. What statistical test are you using to test this hypothesis?
4. Does this problem call for adirectionaltest or anon-directionaltest?Why?
5. What is the value of the standard error?
6. What is the value of t_stat?
7. What is the number of degrees of freedom for this statistical test?(Provide a numeric value)
8. What is the value of t_critagainst which you will compare t_statfor this hypothesis?
9. Based on these data, can we be 95% confident that the average weekly grocery bill of the population of four-person families in the town is less than the national average of four-person families?(Yes or No).Justify your answer.
10. Using theexactformula (NOT the approximate formula) provided in class, what are the lower and upper bounds of a 95% confidence interval for the average amount spent on food per four-person family in the town? (Provide values accurate to the nearest dollar.)