# Hypothesis test: sample of 100

Consider the following hypothesis test:

HO: µ ≥ 80

Ha: µ < 80

A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use a = .01.

a) x = 78.5

b) x = 77

c) x = 75.5

d) x = 81

https://brainmass.com/statistics/hypothesis-testing/hypothesis-test-sample-460193

#### Solution Preview

Please see the attached MS Word document for the solution to the question posted. Included are the charts and formulas required to solve the problem.

Thank you for using BrainMass.

Answer

The test Statistic is given by Z = (X - u)/(sigma/sqrt(n)) = (X - 80)/(12/sqrt(100))

Significance level = 0.01

Decision rule : Reject the null hypothesis if the p value is less than the significance level.

Details

Z Test of Hypothesis for the Mean

Data

Null Hypothesis m= 80

Level of ...

#### Solution Summary

This solution provides a step by step method for computing test statistic for one sample t test is given in the answer. The sample size and the population standard deviation and p-value is calculated for various sample means.