SOLUTION: Find the P - value for the test statistic z=−1.41 for the following null and alternative hypotheses: H0: The population mean is 50. Ha: The population mean is not equal to 50.

Question 1169891: Find the P - value for the test statistic z=−1.41 for the following null and alternative hypotheses:
H0: The population mean is 50.
Ha: The population mean is not equal to 50.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the area to the left of a z-score of -1.41 is equal to .0792698912.
the critical z-score at the different confidence limits are:
at 90% = plus or minus 1.645
at 95% = plus or minus 1.96
at 99% = plus or minus 2.576

the alpha is the area in the rejection zone.
at 90% = .05 on either end
at 95% = .025 on either end
at 99% = .005 on either end

your z-score is within the confidence limits at 90%, 95%, and 99%.
your test alpha is above the critical alpha limits at 90%, 95%, and 99%.

your z-score does not support rejection of the null alternative because your statistical results are not significant enough.

they would be significant if the z-score was above the critical threshold or the alpha was below the critical threshold.

the critical threshold is set before the test is made.

there is not enough evidence to support the alternative hypothesis that the mean is not equal to 50.

the tester is the one who sets the confidence limits.
in order for your test to pass the critical threshold, the critical z-score would have had to be less than plus or minus 1.41 and your critical alpha would have had to be more than .0792698912.

that would have required a two tailed confidence level of .841460173 or less.

while there's nothing to stop the tester from setting a confidence limit so low, it's not typically done.

the higher the confidence limit, the greater the confidence that the results are valid.

here's a reference on critical z-scores and alphas.

https://www.statisticshowto.com/probability-and-statistics/find-critical-values/

here's a reference on confidence limits.

https://www.statisticshowto.com/probability-and-statistics/confidence-interval/

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