Assume the following information for equalsized samples and

Assume the following information for equal-sized samples and make the appropriate t tests

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determine the probability of the t test results and decide whether you would accept of reject the hypothesis of no difference between two groups in each case

Assume the following information for unequal-sized samples and make the appropriate t tests

determine the probability of the t test results and decide whether you would accept of reject the hypothesis of no difference between two groups in each case

Solution

Let mu1 be the mean for group 1

Let mu2 be the mean for group 2

The test hypothesis:

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1 not equal to mu2 (i.e. alternative hypothesis)

The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(25-23)/sqrt(27.8^2/15+27.8^2/15)

=0.197

It is a two-tailed test.

The degree of freedom =n1+n2-2=15+15-2=28

The p-value= P(t with df=28 >0.197) =0.4226 (from student t table)

Assume that the significant level a=0.05

Since the p-value is larger than 0.05, we do not reject Ho.

We would not accept of reject the hypothesis of no difference between two groups in each case

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The test statistic is

t=(25-23)/sqrt(27.8^2/30+27.8^2/15)

=0.228

The degree of freedom =n1+n2-2=30+15-2=43

The p-value= P(t with df=43 >0.228) =0.4104 (from student t table)

Since the p-value is larger than 0.05, we do not reject Ho.

We would not accept of reject the hypothesis of no difference between two groups in each case