Question

1. The average amount of time it takes to complete a particular Sociology test is 86.5 minutes. In a recent study of 26 individuals that took the particular Sociology test, the average amount of time to complete the Sociology test was 83.4 minutes. The sample standard deviation was 8.7 minutes. At the 0.10 level of significance, can it be concluded that the average amount of time it takes to complete the particular Sociology test is less than 86.5 minutes? Show step by step: critical value, compute test value, and conclusion

2. The average annual rainfall in a particular city is 37.4 inches. In a random sample of the last 38 years, it was revealed that the average annual rainfall was 38.2 inches. The population standard deviation of the average annual rainfall in the particular city is 4.7 inches. At the 0.04 level of significance, can it be concluded that the average annual rainfall in the particular city is greater than 37.4 inches? Show step by step: critical value, compute test value, and conclusion

Answer 1

We would be looking at the first question here as:

Q1) As we are testing here whether the mean is less than 86.5 minutes, therefore for 0.1 level and n - 1 = 25 degrees of freedom, we have from the t distribution tables here:
P( t₂₅ < -1.316) = 0.1

Therefore -1.316 is the critical value here.

The test statistic here is computed as:

As the test statistic value here is -1.8169 < -1.316, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the average amount of time it takes to complete the particular Sociology test is less than 86.5 minutes