The mean of a random variable $X$ is denoted by $\mu$. A sample of 50 random observations of \(X

Question

The mean of a random variable $X$ is denoted by $\mu$. A sample of 50 random observations of $X$ is taken and the results are summarised by $\sum x = 527.1$. It is given that the population variance is 15. Carry out a 2-tail test of the null hypothesis $\mu = 9.5$, at the 5% significance level. It is given instead that $\sum x^2 = 6172.31$. In a 1-tail test of the null hypothesis $\mu = 11.5$, the alternative hypothesis is accepted. State the alternative hypothesis, and find an inequality satisfied by the significance level of the test.

Accepted Answer

(a) $\text{ do not reject } H_0, \quad$ (b) $H_1 : \mu < 11.5, \alpha \ge 2.80 $

Hypothesis Testing

Hypothesis Testing