Question

Write mu for the mean of a Normal distribution. The value of the standard deviation is unknown. We want to test H0: mu = 8 vs H1: mu > 8. A random sample of 15 observations is taken from this distribution, and the sample mean (x-bar) and sample standard deviation (s) are calculated. Then t = (x-bar - 8)/[s/square_root(15)] is calculated, and is found to equal = 1.85. At what levels of significance could we reject H0

Answer 1

The given hypothesis is a one sided, right - tailed test

and also given is the number of samples = 15

and the value of test statistic, t = 1.85

The test statistic follows t - distribution (with (n - 1) degrees of freedom) under the null hypothesis

If the value of the test statistic is greater than the critical value.

At 1% significance level, = 0.01

The Critical value, t0.01, 14 = 2.6 > t , hence, we fail to reject the null hypothesis

At 5% significance level, = 0.05

The Critical Value, t0.05, 14 = 1.76 < t , hence, the null hypothesis is rejected

At 10% significance level, = 0.1

The Critical Value, t0.1, 14 = 1.35 < t , hence, the null hypothesis is rejected

At 20% significance level, = 0.2

The Critical Value, t0.2, 14 = 0.87 < t , hence, the null hypothesis is rejected

Therefore, at significance levels of 5%, 10% and 20% the null hypothesis could be rejected