SOLUTION: A paired difference experiment produced the following results: nD=49, x1= 176, x2= 183, xD=−7, sD=58, (a) Determine the rejection region for the hypothesis H0:μD=0 if Ha:μD

Question 1193449: A paired difference experiment produced the following results:
nD=49, x1= 176, x2= 183, xD=−7, sD=58,
(a) Determine the rejection region for the hypothesis H0:μD=0 if Ha:μD>0. Use α=0.03
- t> ____. (5 sig. figs)
(b) Conduct a paired difference test described above.
- The test statistic is ______. (5 sig. figs)

Answer by yurtman(42) (Show Source): You can put this solution on YOUR website!
**a) Determine the Rejection Region**
* **Hypotheses:**
* H0: μD = 0 (Null Hypothesis: Mean difference is zero)
* Ha: μD > 0 (Alternative Hypothesis: Mean difference is greater than zero)
* **Significance Level (α):** 0.03
* **Degrees of Freedom (df):** nD - 1 = 49 - 1 = 48
* **Find the Critical Value (t-critical) using a t-distribution table or statistical software:**
* For a one-tailed test with α = 0.03 and df = 48, t-critical ≈ 1.8856
* **Rejection Region:**
* t > 1.8856
**b) Conduct the Paired Difference Test**
* **Calculate the Test Statistic (t-statistic):**
* t = (xD - μD) / (sD / √nD)
* t = (-7 - 0) / (58 / √49)
* t = -7 / (58 / 7)
* t = -0.85087
**Therefore:**
* **Rejection Region:** t > 1.8856
* **Test Statistic:** t = -0.85087
**Conclusion:**
Since the calculated t-statistic (-0.85087) does not fall within the rejection region (t > 1.8856), we **fail to reject the null hypothesis (H0)**.
There is **not enough evidence** to conclude that the mean difference (μD) is significantly greater than zero at the 0.03 significance level.

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