Question

# 6.71 Hypotheses. Each of the following situations requires a significance test about a population mean m....

6.71 Hypotheses. Each of the following situations
requires a significance test about a population mean m.
State the appropriate null hypothesis H0 and alternative
hypothesis Ha in each case.
(a) 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.
(b) 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.
(c) Many studies have shown that the content of
many herbal supplement pills are not filled with what
is advertised but rather have significant 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%.

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