Given the following hypotheses: H 0 : 12 H 1 : > 12 A random sample of 10 observ

Question

Given the following hypotheses:

H0: 12

H1: > 12

A random sample of 10 observations is selected from a normal population. The sample mean was 11 and the sample standard deviation 5.1. Using the 0.05 significance level:

A. State the decision rule. (Round your answer to 3 decimal places.)

Reject H0 is t > ?

B. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.)

C. What is your decision regarding the null hypothesis?

(Reject/Cannot Reject)H0. There is (Sufficent/Insufficent) evidence to conclude that the population mean is greater than 12?

Explanation / Answer

Solution:

df=n-1=10-1=9

alpha=0.05

alpha/2=0.025

Reject Ho if t >2.262

Solutionb:

t=sample mean-popmean/samplesd/sqrt(sample size)

=11-12/5.1/sqrt(10)

=-0.620

t=-0.620

SOlutionc:

take absolute of t cal

|t|=|-0.620|

=0.620

t cal<t crit

Fail to Reject Null hypothesis

cannot reject Ho

There is insufficent evidence to conclude that the population mean is greater than 12

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