Assume that you have a sample of n, -4, with the sample mean X, 46, and a sample
ID: 3366393 • Letter: A
Question
Assume that you have a sample of n, -4, with the sample mean X, 46, and a sample standard deviation of S, 7, and you have an independent sample of n2 7 from another population with a sample mean of X2-34 and the sample standard de ation S2 8 Assuming the population variances are equal at the 0 01 level of significance, is there evidence that ?? > i ? Deterrnine the hypotheses. Choose the correct answer below Find the test statistic STAT 1?(Round to two decimal places as needed ) Find the p-value. p-value(Round to three decimal places as needed.) Choose the correct condlusion below Reject Ho Reject Ho There is insufficient evidence that ?? ?2 There is sufficient evidence that ?? 12 A. B.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1< u2
Alternative hypothesis: u1 > u2
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 4.625
DF = 9
t = [ (x1 - x2) - d ] / SE
t = 2.59
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 2.59
Therefore, the P-value in this analysis is 0.013.
Interpret results. Since the P-value (0.013) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that u1 > u2.
Reject H0.