Given that "n=400, \\bar{X}=1570, \\sigma=150, \\mu_0=1600"
The following null and alternative hypotheses need to be tested:
"H_0: \\mu=1600"
"H_a:\\mu\\not=1600"
"n=400>30, \\sigma" is known "=>z-test."
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is "\\alpha=0.01," and the critical value for a two-tailed test is "z_c=2.58"
The rejection region for this two-tailed test is "R=\\lbrace z:|z|>2.58\\rbrace."
The z-statistic is computed as follows:
Since it is observed that "|z|=4>2.58=z_c", it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
Two-tailed test
"2P(Z\\leq -4)=0.00006334"
The p-value is p = 0.00006334 and since "p=0.00006334<0.01," it is concluded that the null hypothesis is rejected.
It is concluded that the null hypothesis "H_0" is rejected. Therefore, there is enough evidence to claim that the population mean "\\mu" is different than 1600, at the 0.01 significance level.
The 99% confidence interval is
Comments
Leave a comment