Question

An automobile manufacturing company, while introducing a new model of car during 2007, claimed that the model is fuel efficient as compared to the old model which average 10.5km ler litre with standard deviation of 3.5km. the first 50 cars which came out of the factory were tested for fuel efficiency under normal conditions and found to average 11.3km per litre. Would you conclude that the new model is fuel efficient?

Answer 1

$\mu=10.5, \sigma=3.5, n=50, \bar{x} =11.3\\ Formulate\ the \ hypothesis\\ H_0:\mu=10.5\\ H_1:\mu>10.5\\ This \ is \ a\ one\ tailed\ test\\ \alpha=0.05\\ Since\ \sigma \ is \ known\ we\ are\ using\ the\ z\ test\\ 1-0.05=0.95,\ from\ z-tables\ we \ have\ 1.645\\ The\ z\ critical\ value(s)\ is\ 1.645\\ z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{11.3-10.5}{\frac{3.5}{\sqrt{50}}}=1.616\\ Since\ the\ test\ statistics\ is \,less \ than\ the\ critical\ value,\ that\ is\ 1.616\lt1.645\\ We\ fail\ to\ reject\ the\ the\ null\ hypothesis\ and\ conclude\ that\ the\ new\ model\ is\ not\ fuel\ efficient\\ as\ compared\ to\ the\ old\ model\ with\ average\ of\ 10.5km\ per\ litre\ at\ 5\%\ level\ of significance.$