Question

1. A previous study has shown that the mean number of traffic accidents in medium sized American cities per month is 32. You believe that the number is higher for medium sized cities in your state. You collect information from 125 cities in your state that show a mean number of accidents of 36, with a standard deviation of 3. Are there significantly more accidents in your state than the national average of 32?
2. What is your estimate for the actual population mean number of traffic accidents in medium sized cities in your state?

• For large samples one sample t-tests (n >120) use critical t scores of ±1.96 (for 95% confidence level two tailed test) or ±1.65 (for 95% confidence level one tailed test).
• For small samples (n<120) use critical t score obtained from t-distribution table. You will need to calculate degrees of freedom, which is simply the sample size minus 1 (df = n-1) and use an alpha value of .05.
• For comparing means between two samples (regardless of sample sizes), use an independent samples t-test, with a critical t of ±1.96.

Answer 1

We consider a large sample t test->Critical value =

As t*>1.96, we reject H0

Hence, we say that the traffic accdets are higher for medium sized cities.