Question

A researcher is reviewing 26 UAS accidents and wants to prove that human error involving unsafe acts are mainly due to preconditions. Of the accident information two variables were selected to prove the Hypothesis that preconditions for unsafe acts are a greater factor than unsafe supervision. Using the provided data answer the following and show results of each step. 1. Determine normality 2. What statistical Test is most appropriate 3. Determine if the hypothesis is true 4. What test should you use to show validity of hypothesis results 5. Show all results using either mini tab, excel or stat crunch.

DoD HFACS USAF Accidents Preconditions Supervision 20 13 57 8 9 2 1 18 10 2 1 6 24 1 4 1 4 1 6 2 6 2 4 7 1 1 1 2

Answer 1

Solution:-

2) t-test for two samples would be appropriate.

Preconditions Supervision Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 10.57143 Mean 4.714286 4.036529 Standard Error 5 Median 1 Mode 1.39634 15.10331 Standard Deviation 5.224625 228.1099 Sample Variance27.2967 2.243953 1.672912 17 7.276698 Kurtosis 2.573301 Skewness 56 Range 1 Minimum 57 Maximum 18 148 Sum 14 Count 14

3) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μ_Precondition< μ_Supervision
Alternative hypothesis: μ_Precondition > μ_Supervision

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees offreedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 4.271
DF = 26

t = [ (x₁ - x₂) - d ] / SE

t = 1.37

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 1.37. We use the t Distribution Calculator to find P(t > 1.37) = 0.091

Therefore, the P-value in this analysis is 0.091.

Interpret results. Since the P-value (0.091) is greater than the significance level (0.05), we cannot reject the null hypothesis.