# Statistical Analysis on Difference in Data Sets

(See attached file for full problem description)

a) In an experiment to determine the effects of drought conditions on a certain variety of potato, the following data on crop yield (g/plant) was obtained:

TREATMENT SAMPLE SIZE MEAN YIELD STANDARD DEVIATION

WATERED 6 376 78.4

UNWATERED 12 234 65.8

Does the data suggest that watering raises the true yield by more than 50g/plant?

b) Ten wooden panels were painted partly with an ordinary paint and partly with a flame-resistant paint. The times, in suitable units, taken to burn through the panels are tabulated below:

PANEL A B C D E F G H I J

Ordinary Paint 12 10 8 20 6 13 7 9 25 15

Flame Resistant Paint 17 16 15 22 13 220 13 18 24 18

Test the hypothesis that the paint does not make any real difference.

c) Research suggests that the discharge of industrial waste into rivers affects water quality. To assess the effect of a particular power plant on water quality, 48 water specimens were taken, half 16km upstream and half 4km downstream of the plant. Alkalinity (mg/l) was determined for each specimen and the results are tabulated below.

LOCATION MEAN STANDARD DEVIATION

UPSTREAM 75.9 1.83

DOWNSTREAM 183.6 1.70

Does this data suggest that the true mean alkalinity is higher downstream than upstream?

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#### Solution Summary

This solution conducts a statistical analysis on the data provided to determine if the null hypothesis is accepted or rejected. The test statistic and p-value are calculated in a step-by-step manner in each case and explanations are provided.