Question

The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristic and publishes its finding in Uniform Crime Reports. According to that document, the mean value lost to purse snatching was \(468 in 2012.For last year, 12 randomly selected purse-snatching offenses yielded the following values lost, to the nearest dollar.

Use a t-test tp decide, at the 5%significance level, whether last year's mean value lost to purse snatching has decreased from 2012 mean. The mean and standard deviation of the data are \)455 and $86.80 respectively.

Short answer

The data does not provide sufficient evidence to conclude that the last year's mean value lost to purse snatching has decreased from the2012 mean.

Step-by-step solution

Step 1. Given information.

Consider the given question,

The significance level is$\alpha =0.05$.

Step 2. State the null and alternative hypothesis.

The null hypothesis is given below,

$H_0:\mu =\$468$

The data does not provide sufficient evidence to conclude that the last year's mean value lost to purse snatching has decreased from the 2012mean.

The alternative hypothesis is given below,

$H_a:\mu >\$468$

The data provide sufficient evidence to conclude that the last year's mean value lost to purse snatching has decreased from the2012mean.

Step 3. Compute the confidence interval.

On using the MINITAB procedure,

1. Choose Stat>Basic Statistics>1-Sample t.
2. In Summarized data, enter the sample size 12 and mean 455.
3. In Standard deviation, enter 86.8.
4. In Perform hypothesis test, enter the test mean as 468.
5. Check Options, enter Confidence level as 95.
6. Choose less than in alternative.
7. Click OK in all dialogue boxes.

Hence, from the MINITAB output, the value of test statistics is -0.52 and the P-value is 0.307.

Step 4. Write the conclusion.

If $P\le \alpha$, then reject the null hypothesis.

The P-value is 0.307which is greater than the level of significance that is $P\left(=0.307\right)>\alpha \left(=0.05\right)$.

Therefore, the null hypothesis is not rejected at 5% level.

It can be concluded that the test results are not statistically significant at 5% level of significance.

On interpreting, we can say that the data does not provide sufficient evidence to conclude that the last year's mean value lost to purse snatching has decreased from the2012 mean.