Question

Listed below are time intervals​ (min) between eruptions of a geyser. The​ "recent" times are within the past few​ years, and the​ "past" times are from 1995. Does it appear that the variation of the times between eruptions has​ changed? Use a 0.05 significance level. Assume that the two populations are normally distributed. Recent 77 88 85 81 61 98 65 84 74 84 85 87 Past 87 92 98 94 68 86 87 98 89 96 94 98 test statistic is? pvalue is?

Answer 1

Two populations are assumed to be normally distributed. We do not know exact value of population standard deviation (or variance). So we shall perform two sample t-test.

Suppose, random number X denotes recent time data while random number Y denotes past time data.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistics is given by

where

Degrees of freedom

Corresponding p-value =  0.01704998    [Using R-code 'pt(-2.580927,22)+1-pt(2.580927,22)']

Level of significance

We reject null hypothesis if

Here we see that

So, we reject the null hypothesis.

Based on the given data we conclude that, it appears that the variation of the times between eruptions has changed.