In order to check for regional bias in a widely used standardized test, researchers checked for a difference in the means of random samples of scores from two regions. The sample mean of the 110 scores from Region 1 was 497 with standard deviation 112. The sample mean of the 100 scores from Region 2 was 511 with standard deviation 114. Let μ1 be the population mean score from Region 1, and let μ2 be the population mean score from Region 2. The researchers assumes the population standard deviations are equal and used the alternative hypothesis Ha:μ1-μ2≠0. If the test statistic is t≈-0.90 and the number of degrees of freedom is 208, what is the p-value for this hypothesis test?

Question

Mathematics

Jadiel Roy

13 September, 18:13

In order to check for regional bias in a widely used standardized test, researchers checked for a difference in the means of random samples of scores from two regions. The sample mean of the 110 scores from Region 1 was 497 with standard deviation 112. The sample mean of the 100 scores from Region 2 was 511 with standard deviation 114. Let μ1 be the population mean score from Region 1, and let μ2 be the population mean score from Region 2. The researchers assumes the population standard deviations are equal and used the alternative hypothesis Ha:μ1-μ2≠0. If the test statistic is t≈-0.90 and the number of degrees of freedom is 208, what is the p-value for this hypothesis test?

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Moreno · Answer 1

p-value = 0.369

Step-by-step explanation:

Test of hypothesis which has its the alternative hypothesis as Ha:μ1-μ2≠0 is a two tailed test. Therefore, P-value for a two-tailed test with test statistic t≈-0.90 and the number of degrees of freedom = 208

P-value = 2 X P (t (208) < - 0.90)

= 2 X 0.1846

= 0.369