We assume that blood pressure, X, has a N(µ,σ2) distribution. To estimate µ and σ, we randomly sampled 9 people and measured their blood pressure. The sample mean and sample standard deviation are ¯ X = 110 and S = 6. Knowing that based on the t(8) distribution, 0.8-quantile = 0.9, 0.85-quantile = 1.1, 0.9quantile = 1.4, and 0.95-quantile = 1.9, answer the following questions.

a. Write down the point estimate for µ along with its standard error.

b. Write down the margin of error at 0.8 con?dence level.

c. Write down the 80% con?dence interval estimation for µ based on this sample.

d. Assume that we want to test the null hypothesis H0 : µ = 120 using a one sample t test, what is the t score?