7. Consider Problem 6 above. Suppose we want to test whether the mean height of houses is less than 10 feet. In the following questions, show work and the appropriate formulas, and use proper notation. (a) Formulate the appropriate null and alternative hypotheses using the appropriate notation. (b) Calculate the value of the test statistic.(c) Use R to nd the exact value for the pvalne. (You do not need to give me any H. code or output here.) Show.r the appropriate probability statements needed for the calculation of the pvalue. (d) Based on your answer in part (c), reach the appropriate conclusions at Ge 2 [l and r1 = 0.10. (e) State the nal conclusion[s) with 1words related to the problem. Use complete English sentences that make sense using as few mathematical symboLs as possible. 6. Here are the heights, in feet, of 8 houses in a certain city: 8.3, 1.3, 7.6, 11.3, 10.1, 10.3, 11.6, 7.9. Assuming the lengths are normally distributed, give a 78% confidence interval for the mean height of houses in the city. Show all the necessary work. Make sure you show the appropriate formula and use proper notation. (Use R here to find the critical value because tables may be incomplete.) (11 points)