Population Mean Hypotheses

• Each of the following paragraphs calls for a statistical test about a population mean m. 
• State the null hypothesis Ho nothing happened, there is no difference) 
• State the alternative hypothesis Ha (something happened, there is a difference) in each case. 

(a) The diameter of a spindle in a small motor is supposed to be 5 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target. 

(b) Census Bureau data show that the mean household income in the area served by a hospital is $42,500 per year. A market research firm questions patients at the hospital. The researchers suspect the mean household income of patients is higher than that of the general population.