4. On the basis of a random sample, the null hypothesis

H0: = 0

is tested against the alternative

H1: = 0

and the null hypothesis is not rejected at the 8% significance level given and a sample of size n with sample mean X n.

(a) Does this necessarily imply that 0 is contained in the 95% confidence interval for ? Why? (2.5 points)

(b) Does this necessarily imply that 0 is contained in the 90% confidence interval for ? Why? (2.5 points)

(c) Suppose now H1: > 0. Does this necessarily imply that 0 is con- tained in the 95% confidence interval for ? Why? (2.5 points)

(d) Suppose now H1: > 0. Does this necessarily imply that 0 is con- tained in the 95% confidence interval for if the observed sample mean is larger than 0? (2.5 points)

P.S. When referring to the standard normal table, if the number needed is between the 2 numbers presented on the table, either use interpolation or just use the closer value. Also, if the critical value is beyond (i.e. z 3.49, assume the cumulative probability as 1.