Chapter 9: Problem 5 Previous Problem Problem List Next Problem Results for this

Question

Chapter 9: Problem 5 Previous Problem Problem List Next Problem Results for this submission Entered Answer Preview Result 0.028524 0.028524 incorrect 0.028524 0.028524 correct At least one of the answers above is NOT correct. (1 point) (a) Find the P-value for the test statistic z = 2.19 for the following null and alternative hypotheses: Ho: The population mean is 5. Ha: The population mean is less than 5 The P - value is 0.028524 (b) Find the P-value for the test statistic z = 2.19 for the following null and alternative hypotheses: Ho: The population mean is 5. Ha: The population mean is not equal to 5 The P - value is 0.028524

Explanation / Answer

a) p-value = P(Z < 2.19) = 0.9857

We have decided p-value from alternative hypothesis (Ha).

We need to find p-value for left tail area. So we can use

Z < z test statistic

b) p-value = 2 * P(Z > 2.19 ) = 2 * ( 1 - P( Z<2.19) )

= 2 * ( 1 - 0.9857 )

= 2 * 0.0143

p-value = 0.0286

Note :-  

When you do a two-tailed test you are in fact obtaining both the positive and the negative of the statistic. Remember a two-tailed test means that your are testing whether your alternative hypothesis is different from the null, which could mean either greater or less than. The "greater than" part gives you the critical region on the positive side of the curve, whereas the "less than" part gives you other critical region on the negative side of the curve.

Since both regions are the same, you will usually only use either of the statistics (positive or negative) and divide your level of significance in half to account for the other side.

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