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QUESTION 2 [13 MARKS] A research is conducted to investigate the prevalence of airborne bacteria in carpeted and uncarpeted rooms in a hospital. Eight samples of room air from both rooms were pumped over a Petri dish and incubated for three hours before the number of bacteria formed on each Petri dish were measured (in bacteria per cubic foot of air). A statistical analysis of the data using Microsoft Excel is illustrated in Figure 1. Assume that the number of bacteria has a normal distribution. *-Test: Two-Sample Assuming Equal Variances Carpeted Uncarpeted Mean 10.95 8.325 Variance 6.5257 15 2193 Observations 8 B Pooled Variance 10.8725 Hypothesized Mean Difference 0 14 t Stat 1.5922 P(Text) one-tail 0.0668 Critical one-tail 1 8875 P(Test) two-tail 0.1337 Critical two-tail 2 2638 Figure 1 Conduct a necessary analysis to show that the number of bacteria formed in both carpeted and uncarpeted rooms have equal population variances at 4% level of significance. Use confidence interval approach. [8 Marks] It is claimed that the carpeted rooms are more likely to accumulate more bacteria compared to uncarpeted rooms. Test this claim at 4%% level of significance using P-value approach. [5 Marks]