Each of the following situations requires a significance test about a population mean . State the appropriate null hypothesis and alternative hypothesis in each case.
David’s car averages 28 miles per gallon on the highway. He now switches to a new motor oil that is advertised as increasing gas mileage. After driving 2500 highway miles with the new oil, he wants to determine if his gas mileage actually has increased.
The diameter of a spindle in a small motor is supposed to be 4 millimeters. If the spindle is either too small or too large, the motor will not perform properly. The manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target.
Many studies have shown that the content of many herbal supplement pills are not filled with what is advertised but rather have signifcant amounts of filler material such as powdered rice and weeds.17 The percentages of real produce versus filler vary by company. A consumer advocacy group randomly selects bottles and tests each pill for its percentage of ginseng. The group is testing the pills to see if there is evidence that the percent of ginseng is less than 90%.