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

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=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}`

i.e.
`t=(50-46)/((8)/(√(25)))=2.5`

Hence, the observed critical value = 2.5