Question

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%.

Answer #1

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