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# Hypothesis test : t test

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether
there are more units produced on the afternoon shift than on the day shift. A sample of 54
day-shift workers showed that the mean number of units produced was 345, with a standard
deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number
of units produced was 351, with a standard deviation of 28 units. At the .05 significance
level, is the number of units produced on the afternoon shift larger?

Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming
America's Cup race. They race over a part of the course several times. Below are the
sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?
Boat Times (minutes)
Prada (Italy) 12.9 12.5 11.0 13.3 11.2 11.4 11.6 12.3 14.2 11.3
Oracle (U.S.A.) 14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 19.0
For many years TV executives used the guideline that 30 percent of the audience were
watching each of the prime-time networks and 10 percent were watching cable stations on
a weekday night. A random sample of 500 viewers in the Tampa-St. Petersburg, Florida,
area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to
the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station.
At the .05 significance level, can we conclude that the guideline is still reasonable?

A study regarding the relationship between age and the amount of pressure sales personnel
feel in relation to their jobs revealed the following sample information. At the .01 significance
level, is there a relationship between job pressure and age?

Degree of Job Pressure
Age (years) Low Medium High
Less than 25 20 18 22
25 up to 40 50 46 44
40 up to 60 58 63 59
60 and older 34 43 43

#### Solution Summary

The solution provides step by step method for the calculation of t test . Formula for the calculation and Interpretations of the results are also included.

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