Question

The following 14 numbers are generated by a computer using a N(u, standard deviation²) model.
49.62 55.87 44.59 54.38 55.80 55.85 53.11
53.34 49.12 47.80 55.28 49.27 48.72 43.66
we wish to test H0 : u = 55 vs. HA : u is not = 55.
1. compute x and s²;
2. compute the t-statistic;
3. give an accurate p-value using SAS;
4. draw your conclusion by conducting your t-test at the 5% significance level;
5. construct a 95% confidence interval for u.

Answer 1

1)
xbar = 51.17
s^2 = 17.5668

b)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (51.17 - 55)/(4.1913/sqrt(14))
t = -3.419

3)
P-value Approach
P-value = 0.0046

4)
As P-value < 0.05, reject the null hypothesis.

5)
sample mean, xbar = 51.17
sample standard deviation, s = 4.1913
sample size, n = 14
degrees of freedom, df = n - 1 = 13

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.16

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (51.17 - 2.16 * 4.1913/sqrt(14) , 51.17 + 2.16 * 4.1913/sqrt(14))
CI = (48.75 , 53.59)