Question

Consider the following hypothesis test. H0: μ = 15 Ha: μ ≠ 15 A sample of 50 provided a sample mean of 14.11. The population standard deviation is 3. Find the value of the test statistic. (Round your answer to two decimal places.)

Answer 1

Answer: -2.10

Step-by-step explanation:

Given : $H_0:\mu=15$

$H_a:\mu\neq15$

Sample size : n= 50, since the sample size is greater than 30 , so we apply z-test.

Sample mean : $\overline{x}=14.11$

Standard deviation : $\sigma= 3$

The test statistic for population mean :-

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

i.e. $z=\dfrac{14.11-15}{\dfrac{3}{\sqrt{50}}}=-2.09775011752\approx-2.10$

Hence, the value of the test statistic = -2.10