Question

This is the question:Conduct a hypothesis test to see if the mean property crime rates for 1960 through 1981 (collectively) are different from the mean property crime rates from 1982 through 2012 (collectively).

Can you check my hypothesis for accuracy?  

Ho: ?1 ? ?2 = 0

Ho: ?1 ? ?2 ? 0

The null hypothesis is the mean property crime rates for 1960 through 1981 is equal to the mean property crime rates from 1982 through 2012.

The alternative hypothesis is the mean property crime rates for 1960 through 1981 daily is not equal to the mean property crime rates from 1982 through 2012

Next Question: Do I use a t-test for two sample asuming equal variances?

Answer 1

the null and alternative hypothesis is correct.

The null hypothesis, Ho: the mean property crime rates for 1960 through 1981 is equal to the mean property crime rates from 1982 through 2012. ?1 ? ?2 = 0

The alternative hypothesis, H1: the mean property crime rates for 1960 through 1981 daily is not equal to the mean property crime rates from 1982 through 2012. ?1 ? ?2 ? 0

the two groups are related to each other as it is a time series data. Hence it is suggested to apply paired T test.

Test Statistic

Critical value

• -t(a/2,n-1),t(a/2,n-1) (Two tailed test

P-value

• 2*(1-P(T?|t|) (Two tailed test)

Decision rule

• Reject Ho if |t| > t(a/2, df) or p-value < alpha (two tailed test)