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 find the exact value for the p-value. (You do not need to give me any R code or output here.) Show the appropriate probability statements needed for the calculation of the p-value. (d) Based on your answer in part (c), reach the appropriate conclusions at o = 0.05 and o = 0.10. (e) State the final conclusion (s) with words related to the problem. Use complete English sentences that make sense using as few mathematical symbols as possible