Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months.
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Answer:
Since the p value is very low compared with the significance level provided 0.01, we have enough evidence to conclude that the true variance and on this case the deviation is significantly lower than 13 at 1% of significance.
Step-by-step explanation:
We have the following data given
represent the sample size selected for the test
represent the confidence level
represent the sample variance obtained
represent the value that we want to test
System of hypothesis
We want to review if the population deviation is significantly lower than 13 and we can check this with the variance, the system of hypothesis would be:
Null Hypothesis:
Alternative hypothesis:
Statistic
To test this hypothesis the statistic is:
The degrees of freedom for this case are:
Replacing in the statistic formula we got:
P value
since we have a left tailed test the p value would be givne by:
We can find the p value with this excel code:
"=CHISQ.DIST(5.206,24,TRUE)"
Since the p value is very low compared with the significance level provided 0.01, we have enough evidence to conclude that the true variance and on this case the deviation is significantly lower than 13 at 1% of significance.