1.) Set Up Hypothesis and Determine Level of Significance:
Null Hypothesis (H0): There is no difference in the mean number of symptoms of Computer Vision Syndrome based on the number of hours spent in front of a computer.
Alternative Hypothesis (Ha): There is a difference in the mean number of symptoms of Computer Vision Syndrome based on the number of hours spent in front of a computer.
Level of Significance: α = 0.05
2.) Select the Appropriate Test Statistic:
Since we are comparing the means of two independent samples, we will use the two-sample t-test.
3.) Set Up the Decision Rule:
Since the level of significance is α = 0.05, we will use a two-tailed test. The critical value for a two-tailed test with α = 0.05 is ±2.093.
4.) Compute the Test Statistic:
The formula for the two-sample t-test is:
t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))
Where:
x1 = mean number of symptoms for ≥ 5 HRS of Computer Time = 5.2
x2 = mean number of symptoms for < 5 HRS of Computer Time = 4.8
s1 = standard deviation of symptoms for ≥ 5 HRS of Computer Time = 1.3
s2 = standard deviation of symptoms for < 5 HRS of Computer Time = 0.9
n1 = number of observations for ≥ 5 HRS of Computer Time = 10
n2 = number of observations for < 5 HRS of Computer Time = 10
Plugging in the values:
t = (5.2 - 4.8) / sqrt((1.3^2 / 10) + (0.9^2 / 10))
5.) Conclusion:
Compare the computed test statistic (t) with the critical value. If the computed test statistic falls within the critical region, we reject the null hypothesis. If it falls outside the critical region, we fail to reject the null hypothesis.
Note: The actual computation of the test statistic and conclusion is not provided in the given text.