a) A video producer wants to determine whether the 2 types of microelectronic circuits it uses have the same flow rates. The research engineer has obtained the following data. Interpret the result at a 10% significance level. (Assuming the variances are not equal.)
1st design 2nd design
Sample mean (Ẋ) 24.2 23.9
Sample standard deviation (S) 3.16 4.47
Number of observations (n) 15 12
The research engineer can use a two-tailed t-test to compare the two designs. The null hypothesis is that the two designs have the same flow rate, and the alternative hypothesis is that the two designs have different flow rates.
The t-statistic is calculated as follows:
t = (Ẋ1 - Ẋ2) / (S1^2/n1 + S2^2/n2)^0.5
t = (24.2 - 23.9) / (3.16^2/15 + 4.47^2/12)^0.5
t = 0.3 / (9.9 + 20.2)^0.5
t = 0.3 / 5.9
t = 0.05
The critical value for a two-tailed t-test at a 10% significance level is 2.228. Since the calculated t-statistic is less than the critical value, we fail to reject the null hypothesis. This means that the two designs have the same flow rate.