SOLUTION: The average length of the time for people to vote using the old procedure during the presidential election period in election precinct A is 30 minutes. Using computerization as a

Question 1180643: The average length of the time for people to vote using the old procedure during
the presidential election period in election precinct A is 30 minutes. Using
computerization as a new election method, a random sample of 25 registrants was used
and found to have a mean length of voting time to 24 minutes with a sample standard
deviation of 2.9 minutes. Test the hypothesis in which the population mean is less than
the sample mean.
Solution:
1. H0:
H1:
2. Level of Significance:
3.Test:
4. Critical Region:
5. Solutions:
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**1. Hypotheses:**
* **Null Hypothesis (H0):** The population mean voting time using the new computerized method is greater than or equal to the old average (μ ≥ 30).
* **Alternative Hypothesis (H1):** The population mean voting time using the new computerized method is less than the old average (μ < 30). This is what we want to test.
**2. Level of Significance:**
* You didn't specify a level of significance, so let's use a common one: α = 0.05
**3. Test Statistic:**
Since we have a small sample size (n = 25) and we don't know the population standard deviation, we'll use a t-test.
* **t = (x̄ - μ) / (s / √n)**
where:
* x̄ = sample mean (24 minutes)
* μ = population mean under the null hypothesis (30 minutes)
* s = sample standard deviation (2.9 minutes)
* n = sample size (25)
* **Calculate t:**
t = (24 - 30) / (2.9 / √25) = -6 / 0.58 ≈ -10.34
**4. Critical Region:**
Since this is a one-tailed test (H1: μ < 30), we need to find the critical t-value for α = 0.05 and degrees of freedom (df) = n - 1 = 24.
* Using a t-table or calculator, the critical t-value is approximately -1.711.
* **Critical Region:** t < -1.711
**5. Decision and Conclusion:**
* Our calculated t-value (-10.34) falls in the critical region (t < -1.711).
* Therefore, we **reject the null hypothesis (H0)**.
* There is sufficient evidence to support the claim that the population mean voting time using the computerized method is less than the old average of 30 minutes.
**In simpler terms:** The sample data provides strong evidence that the new computerized voting method is faster than the old procedure.
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