You are conducting a between-subjects test with an n of 15 per group, Mean A = 8
ID: 3043732 • Letter: Y
Question
You are conducting a between-subjects test with an n of 15 per group, Mean A = 83 and Mean B = 71. The standard deviation for each group is 8. Calculate the appropriate t-test. You can use previously calculated values where appropriate. (2 marks) If you had a non-directional hypothesis in this study, would your t-test be significant? Make sure that you provide the critical value you used in making this decision. (2 marks) If you had a directional hypothesis where you predicted that Mean A would be greater than Mean B, would your t-test be significant? Make sure that you provide the critical value you used in making this decision. (2 marks) Would you expect your power to increase, decrease, or remain the same relative to question 1? Explain your reasoning. (2 marks) Would you expect your Type II error to increase, decrease, or remain the same relative to question 1? Explain your reasoning. (2 marks)You are conducting a between-subjects test with an n of 15 per group, Mean A = 83 and Mean B = 71. The standard deviation for each group is 8. Calculate the appropriate t-test. You can use previously calculated values where appropriate. (2 marks) If you had a non-directional hypothesis in this study, would your t-test be significant? Make sure that you provide the critical value you used in making this decision. (2 marks) If you had a directional hypothesis where you predicted that Mean A would be greater than Mean B, would your t-test be significant? Make sure that you provide the critical value you used in making this decision. (2 marks) Would you expect your power to increase, decrease, or remain the same relative to question 1? Explain your reasoning. (2 marks) Would you expect your Type II error to increase, decrease, or remain the same relative to question 1? Explain your reasoning. (2 marks)
You are conducting a between-subjects test with an n of 15 per group, Mean A = 83 and Mean B = 71. The standard deviation for each group is 8. Calculate the appropriate t-test. You can use previously calculated values where appropriate. (2 marks) If you had a non-directional hypothesis in this study, would your t-test be significant? Make sure that you provide the critical value you used in making this decision. (2 marks) If you had a directional hypothesis where you predicted that Mean A would be greater than Mean B, would your t-test be significant? Make sure that you provide the critical value you used in making this decision. (2 marks) Would you expect your power to increase, decrease, or remain the same relative to question 1? Explain your reasoning. (2 marks) Would you expect your Type II error to increase, decrease, or remain the same relative to question 1? Explain your reasoning. (2 marks)
Explanation / Answer
Solution:-
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 two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it 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 = 2.9212
DF = 28
t = [ (x1 - x2) - d ] / SE
t = 4.11
tcritical = 2.05
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size 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 the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 28 degrees of freedom is more extreme than 4.11; that is, less than -4.11 or greater than 4.11.
Thus, the P-value = less than 0.0001.
Interpret results. Since the t-value (4.11) is greater than the tcritical (2.05), we cannot accept the null hypothesis.
If we had a non-directional hypothesis in this study, then our t-test would be significant.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: A< B
Alternative hypothesis: A > B
t = 4.11
tcritical = 1.70
Interpret results. Since the t-value (4.11) is greater than the tcritical (1.70), we cannot accept the null hypothesis.
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.
If we had a directional hypothesis where you predicted that Mean A would be greater than Mean B, then our t-test would be significant.
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