You wish to test the following claim (Ha) at a significance level of ?-0.10 You

Question

You wish to test the following claim (Ha) at a significance level of ?-0.10 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 equal. You obtain a sample of size n1 22 with a mean of M1 77.8 and a standard deviation of SD = 12.7 from the first population. You obtain a sample of size n2 22 with a mean of M2 = 81.2 and a standard deviation of SD2 15.2 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the conservative under estimate for the degrees of freedom as mentioned in the textbook. (Report answer accurate to four decimal places.) p-value- The p-value is. less than (or equal to) ? greater than ? The tact ctatietin loade tn rlonieinn t accurate

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.

Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = 4.22294
DF = 42

t = [ (x1 - x2) - d ] / SE

t = - 0.805

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 - 0.805

Therefore, the P-value in this analysis is 0.213

Interpret results. Since the P-value (0.213) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that there is significance difference

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.