Professor bond claims her mean test score is a 80 - but you worry it's lower than that. to test upper h 0 : mu equals 80 versus upper h subscript a baseline : mu less than 80 a simple random sample of size nequals35 is obtained. complete parts a through e below. click here to view the t-distribution area in right tail. (a) does the population have to be normally distributed to test this hypothesis? why? a. yes, because n> 30. b. no, because the test is two-tailed. c. yes, because the sample is random. d. no, because n> 30. (b) if x overbarequals77.5 and sequals5.8, compute the test statistic. the test statistic is t*equals nothing. (round to two decimal places as needed.) (c) approximate the p-value. choose the correct answer below. a. p-valueless than0.005 b. 0.005less thanp-valueless than0.01 c. 0.01less thanp-valueless than0.025 d. 0.025less thanp-valueless than0.05 (d) if the researcher decides to test this hypothesis at the alphaequals0.05 level of significance, will the researcher reject the null hypothesis? no, there is insufficient evidece to prove the mean score is less than professor bond states. yes, there is sufficient evidence to prove the mean score is less than professor bond states. click to select your answer(s) and then click check answer.