ConsiderH0:=27versusH1:27. A random sample of36observations taken from this population produced a sample mean of24.89. The population is normally distributed with=6.

Note: Use Table IV in Appendix C to compute the probabilities.

(a)Calculate thep-value.

(b)Considering thep-value of part (a), would you reject the null hypothesis if the test were made at the significance level of 0.05?

(c)Considering thep-value of part (a), would you reject the null hypothesis if the test were made at the significance level of 0.01?

Recall the following from section 9.2 of the text.

Thep-value or probability-value approach.

(1) Werejectthe null hypothesis ifp-value orp-value.

Wedo not rejectthe null hypothesis ifp-value >or<p-value.

(2) For aone-tailed test, thep-value is given by the area in the tail of the sampling distribution curve beyond the observed value of the sample statistic.

For atwo-tailed test, thep-value is given bytwicethe area in the tail of the sampling distribution curve beyond the observed value of the sample statistic.

(3) To find the area in the tail of the sampling distribution curve (we use normal distribution here), we first find the value ofzcorresponding to the observed value of

using the formula:

where

n= sample size, andandare the population mean and standard deviation. We call thiszvalue theobserved value ofz.

8th-ed Chapter 09, Section 9.2, Intelligent Tutoring Problem 018

Partially correct answer icon

Your answer is partially correct.

ConsiderH0:=27versusH1:27. A random sample of36observations taken from this population produced a sample mean of24.89. The population is normally distributed with=6.

(a)Compute

Round the answer to four decimal places.

Enter you answer in accordance to the item a) of the question statement

(b)Computezvalue. Round the answer to two decimal places.

z=

Enter you answer in accordance to the item b) of the question statement

(c)Find area to the left ofz-value on the standard normal distribution. Round the answer to four decimal places.

The area =

Enter you answer in accordance to the item c) of the question statement

(d)Findp-value. Round the answer to four decimal places.

p-value =

Enter you answer in accordance to the item d) of the question statement