Question

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46. The sample size is 25 and α = .05. If the sample mean is 50 and the population standard deviation is eight, the observed z value is _______.

Answer 1

Answer: 2.5

Step-by-step explanation:

Let $\mu$ be the population mean .

Then, Null hypothesis : $H_0:\mu\leq46$

Alternative hypothesis :  $H_1:\mu>46$

We assume that this is a normal distribution.

Given : Sample size : n=25 , since the sample is small (n<30) so we cannot apply z-test . Thus the test is t-test.

Sample mean : $\overline{x}=50$

Population standard deviation : $\sigma= 8$

The test statistic for population mean is given by :-

$t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

i.e. $t=\dfrac{50-46}{\dfrac{8}{\sqrt{25}}}=2.5$

Hence, the observed critical value = 2.5