Question

7. Suppose the average temperature for the local area during summer was previously known to be 24 degrees Celsius. A local scientist believes that there has been an increase in average temperature from 1996 to 2000, and argues that the average temperature during this period was significantly different from 21 degrees Celsius. The average temperatures during summer recorded from 1996 to 2000 are given as: 25, 27, 22, 27, 23. Performa two-sided t-test for the null hypothesis that Ho : {Mean temperature is 24} at a 5 percent significance level.

Answer 1

We have 5 observations.

H​​​​​​0​​​ : The mean temperature is 24

H​​​​​​1 : The mean temperature is not equal to 24.

For finding the value of t-statistic we need to find sample mean and sample variance. We do that by the following formulae:

Next we find the value of t statistic :

Our hypothetical distribution for T under null hyoothesis is a T distribution with 4 degrees of freedom.

We find the corresponding phvalue for two sided test as p=2.P(T>|t|)

Note that we are using a two sided test, thus we calculate only the upper tail probability from the absolute value of t and multioly that probability with 2 to find the actual probability value of the two tails below and above the cutoff points -t and t.

Here p= 0.476621

This value can be found using the t-tables provided in standard statistics text books, (or the internet). For tables the corresponding tail probabilities are tabulated against degrees of freedom and t value.

We see that p value is much greater than 0.05, thus we fail to reject our null hypothesis. That is there is no significant difference in the average temperature of the given period from 24.