Question

the annual rainfall at a certain place is normally distributed with mean 30. If the rainfall during the past 8 years are 31.1, 30.7, 24.3, 28.1, 27.9, 32.2, 25.4 and 29.1, can we conclude that average rainfall during the past 8 years is less than the normal rainfall ?(LOS 1%)

Answer 1

Hypothesis H0 : µ =30 vs H1 < 30

Then we go ahead test the hypothesis

we first calculate the standard deviation and mean from the given values.

mean = 28.6, standard deviation = 2.76 and standard error = 0.976.

t = (x-µ)/(∂/√n) = (30-28.6)/(2.76/√8) = (1.4/0.976)= 1.43 we calculate from t tables p-value of t 1.43, d f =7,p-value =0. 0979 thus since the p-value is greater than given significance of 0.01 we fail to reject null hypothesis and conclude that the average rainfall is not less than 30.