Question

1. An economist believes that there is a positive correlation between income and percent of disposable income saved by young adults. To test this, a sample of income and saving data is gathered from the Division of Taxation for adults under the age of 35. State the null and the alternative hypothesis to test this claim.

2. The National Highway Safety Administration recognizes that the antilock braking system as a revolutionary safety feature. The claim is that automobiles with this system are involved in fewer fatal crashes than those without. State the null and the alternative hypothesis to test this claim.

Answer 1

Q1) As we are testing here whether there is a positive correlation between income and percent of disposable income saved by young adults, therefore the null and the alternate hypothesis here are given as:

Where r is the correlation between income and percent of disposable income saved by young adults

Q2) As we are testing here whether the automobiles with this system are involved in fewer fatal crashes than those without, therefore here we are comparing 2 means. The null and the alternative hypothesis here are given as:

Where is the mean number of fatal crashes with the system and is the mean number of fatal crashes without the system.