Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test H0 : μ1=μ2 vs Ha : μ1≠μ2 using the sample results x¯1=15.3, s1=11.6 with n1=100 and x¯2=18.4, s2=14.3 with n2=80. a) Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. b) What is the conclusion of the test? Test at a 10% (reject OR do not reject)
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.
Test H0 : μ1=μ2 vs Ha : μ1≠μ2 using the sample results x¯1=15.3, s1=11.6 with n1=100 and x¯2=18.4, s2=14.3 with n2=80.
a) Give the test statistic and the p-value.
Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.
b) What is the conclusion of the test? Test at a 10% (reject OR do not reject)
*Additional info that may be helpful: When choosing random samples of size n1 and n2 from populations with means μ1 and μ2, respectively, the distribution of the differences in the two sample means, x¯1-x¯2, has the following characteristics.
Center: The mean is equal to the difference in population means, μ1-μ2.
Spread: The standard error is estimated using SE=s12n1+s22n2.
Shape: The standardized differences in sample means follow a t-distribution with degrees of freedom approximately equal to the smaller of n1-1 and n2-1.
For small sample sizes (n1<30 or n2<30), the t-distribution is only a good approximation if the underlying population has a distribution that is approximately normal.
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