Consider the following competing hypotheses and accompanying sample data drawn i
ID: 3066573 • Letter: C
Question
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations.
Use Table 2. H0: 1 2 0 HA: 1 2 < 0 = 248 = 250 s1 = 31 s2 = 16 n1 = 11 n2 = 11
a-1. Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic
a-2. Calculate the critical value at the 1% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Critical value
a-3. Do you reject the null hypothesis at the 1% level? Yes, since the value of the test statistic is not less than the critical value. No, since the value of the test statistic is less than the critical value. No, since the value of the test statistic is not less than the critical value. Yes, since the value of the test statistic is less than the critical value.
b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic
b-2. Calculate the critical value at the 1% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Critical value
b-3. Do you reject the null hypothesis at the 1% level? Yes, since the value of the test statistic is not less than the critical value. No, since the value of the test statistic is not less than the critical value. Yes, since the value of the test statistic is less than the critical value. No, since the value of the test statistic is less than the critical value.
Explanation / Answer
Solution:-
a-1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2> 0
Alternative hypothesis: 1 - 2 < 0
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 = 10.51838
DF = 20
t = [ (x1 - x2) - d ] / SE
t = - 0.19
a-2) tcritical = - 2.528
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.
a-3) Interpret results. Since the t-value (- 0.19) is greater than the critical value (-2.19), hence we have to accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that there is significance difference.
No, we do not reject the null hypothesis , since the value of the test statistic is not less than the critical value
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.