Answer to Question #143280 in Statistics and Probability for Margaret

Question

Consider the following hypothesis test
H0 u=50 vs H1 u>50
A sample of 60 is used and the population standard deviation a is 8 when X=52,5. The p-value is
1. 2,4206
2. 0,0078
3. 0,0156
4. 0,9922
5. 0,9918

Answer 1

The provided sample mean is $\bar{x}=52.5,$ and the known population standard deviation is $\sigma=8,$ and the sample size is $n=60.$

The following null and alternative hypotheses need to be tested:

$H_0:\mu=50$

$H_1:\mu>50$

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{52.5-50}{8/\sqrt{60}}=2.42061459$$

The p-value is $p=P(z>2.42061459)=0.007747$

$2.\ \ \ 0.0078$