The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristics and publishes its findings in Population-at-Risk Rates and Selected Crime Indicators. According to that document, the mean value lost to purse snatching was 406 dollars in 2004. This year, the mean and standard deviation of the 32 randomly selected purse snatching offenses are 379.92 dollars and 35.57 dollars, respectively. At the 10% significance level, do the data provide sufficient evidence to conclude that this year’s mean value lost to purse snatching is less than the mean value lost in 2004?

Procedure:

Assumptions: (select everything that applies)

Step 1. Hypotheses Set-Up:

in
 H0:\displaystyle {H}_{{0}}:  = , where is the and the units are
 Ha:\displaystyle {H}_{{a}}:  , and the test is

Step 2. The significance level α=\displaystyle \alpha= %

Step 3. Compute the value of the test statistic: = (Round the answer to 3 decimal places)

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA PVA
Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic:
left CV is and right CV is P-value is

Step 5. Decision:

CVA PVA
Is the test statistic in the rejection region? Is the P-value less than the significance level?

Conclusion:

Step 6. Interpretation:

At 10% significance level we have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

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