Someone please help me with this stats question

Question

You wish to test the following claim (Ha) at a significance level of α=0.05.

Ho:μ=74.1

Ha:μ>74.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=53 with mean M=77.5 and a standard deviation of SD=6.9.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic = __________

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value = __________

NOTE: I have the test statistic, I just need the p-value. I just put the entire question on here for anyone who needs it.

Answer 1

Since we don't know the population standard deviation, the test statistic is

t-stat = (M - mu) / (SD/sqrt(n)) = (77.5 - 74.1)/(6.9/sqrt(53) = 3.59

since it is a right tailed test, the p-value is P(t > t-stat) = P(t > 3.59) with n-1 = 52 degrees of freedom = ~ 0.0004.