You want to know if the number of crimes in your city has exceeded 10 per week. You take a sample of 8 weeks and get an average of 10.5 crimes. It is known that the population standard deviation of the number of crimes per week in your city is 5. Perform the appropriate hypothesis test using a 1% level of significance. You must show the 6 steps of hypothesis testing in your submission to get 1 mark.

(6 steps of hypothesis testing:

1. Set up the hypotheses and check conditions

2. Decide on the significance level,

3. Calculate the test statistic

4. Calculate probability value (p-value), or find the rejection region:

5. Make a decision about the null hypothesis

6. State an overall conclusion)