Question

# You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.       Ho:μ1=μ2Ho:μ1=μ2       Ha:μ1≠μ2Ha:μ1≠μ2...

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.

Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1≠μ2Ha:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data.

Sample #1 Sample #2
 68.6 56 50.4 59.5 56 69.3 52.2 82.8 69.6 69.6 45.7 68.6 65.1 55.5 65.1 70.6
 97.1 55.2 39.5 70.1 95.4 79.5 64.4 78.2 77 74.6 39.5 71.8 74.6 85.5 41.6 32.7 77.6 71.2 91.4 70.7 75.8 47.5 64.9 76.4 59.7

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

(a)

= 0.10

ndf = n1 + n2 - 2 = 16 + 25 - 2 = 39

From Table, critical values of t = 1.6849

(b)

From the given data, the following statistics are calculated:

n1= 16

1 = 62.75

s1 = 9.5392

n2 = 25

2 = 68.476

s2 = 17.5038

Test Statistic is:

t = (62.75-68.476)/4.7868 = - 5.726/4.7868 = - 1.200

So,

test statistic = - 1.200

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