Question

You wish to test the claim that the first population mean is greater than the second...

You wish to test the claim that the first population mean is greater than the second population mean at a significance level of α = 0.002 . H o : μ 1 = μ 2 H a : μ 1 > μ 2 You obtain the following two samples of data.

Sample one

70.3
82.4
62.3
97.4
69.1
63.3
64.7
89.4
81.6
67.6
82.0
51.0
53.4
68.8

73.5

sample2

60.2
61.0
62.8
62.8
75.3
77.4
68.8
61.0

58.5

What is the test statistic for this sample?

test statistic =  Round to 3 decimal places.

What is the p-value for this sample?

p-value =  Use Technology Round to 4 decimal places.

The p-value is...

less than (or equal to) αα

greater than αα



This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null



As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.

There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.

The sample data support the claim that the first population mean is greater than the second population mean.

There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

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Answer #1

We assume population variances are same, then test statistic = = 1.394 n1sample size of sample 1-15 n2 = sample size of sample 2-9. x = sample mean of sample 1 = 71.8. sample mean of sample 2-65.31. s1 = sample sd of sample 1 = 12.8. s2-sample mean of sample 2-6.90 s - pooled sd -1-1)si1)s p-value = P(t > 1.394|t ~ t15+9-2) = 0.0886 The p - value is greater than a0.002 This test statistic leads to a decision to fail to reject the null 11.039.4

There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

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