Question 1200869: 4 A physiological experiment was conducted to study the effect of various factors on pulse rate. For one factor, there were 92 subjects, the mean pulse rate of which was 72.87, and the sample standard deviation was 11.01. Consider the following hypotheses:
i. H0: µ =75 vs. Ha: µ > 75, ii. H0: µ =75 vs. Ha: µ ≠ 75 where µ is the population mean.
a). Compute the p-value for each test .
b)State the conclusion based on the 5% level of significance.
Answer by GingerAle(43)   (Show Source):
You can put this solution on YOUR website! **a) Calculate the p-values**
**i) H0: µ = 75 vs. Ha: µ > 75 (Right-tailed test)**
1. **Calculate the test statistic (t-score):**
* t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
* t = (72.87 - 75) / (11.01 / sqrt(92))
* t ≈ -1.77
2. **Find the p-value:**
* Use a t-distribution table or statistical software to find the p-value associated with the calculated t-score and degrees of freedom (df = sample size - 1 = 91).
* For a right-tailed test and t = -1.77 with 91 degrees of freedom, the p-value is approximately 0.040.
**ii) H0: µ = 75 vs. Ha: µ ≠ 75 (Two-tailed test)**
1. **Calculate the test statistic (t-score):**
* The t-score is the same as in part (i): t ≈ -1.77
2. **Find the p-value:**
* For a two-tailed test, double the p-value obtained in the one-tailed test.
* p-value (two-tailed) = 2 * 0.040 = 0.080
**b) State the conclusions**
**Significance Level (α) = 0.05**
* **i) H0: µ = 75 vs. Ha: µ > 75**
* p-value (0.040) < α (0.05)
* **Reject the null hypothesis (H0).**
* There is sufficient evidence to suggest that the population mean pulse rate is greater than 75.
* **ii) H0: µ = 75 vs. Ha: µ ≠ 75**
* p-value (0.080) > α (0.05)
* **Fail to reject the null hypothesis (H0).**
* There is not enough evidence to conclude that the population mean pulse rate is significantly different from 75.
**In Summary:**
* For the one-tailed test, we have enough evidence to reject the null hypothesis and conclude that the mean pulse rate is likely higher than 75.
* For the two-tailed test, we do not have enough evidence to reject the null hypothesis, meaning we cannot conclude that the mean pulse rate is significantly different from 75.
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