In a laboratory experiment studying photosynthesis, the rate of oxygen production, yyy units per minute, was measured for a random sample of 11 aquatic plants under specific conditions. The recorded rates were:
5,18,22,26,31,35,38,44,49,52,115 5, 18, 22, 26, 31, 35, 38, 44, 49, 52, 115 5,18,22,26,31,35,38,44,49,52,115Find the median and quartiles for these data.
A value that is greater than Q3+1.5×(Q3−Q1)Q_3 + 1.5 \times (Q_3 - Q_1)Q3+1.5×(Q3−Q1) or smaller than Q1−1.5×(Q3−Q1)Q_1 - 1.5 \times (Q_3 - Q_1)Q1−1.5×(Q3−Q1) is defined as an outlier.
Show that 115 is the only outlier.
Draw a box plot for these data on a scale from 0 to 120, indicating clearly the position of the outlier.
The value of 115 is omitted from the sample as it is considered an error in measurement.
Show that SyyS_{yy}Syy for the remaining 10 data points is 1940.
For these same 10 plants, the light intensity, xxx lux, was also measured. For these 10 data points, it is given that Sxx=2500S_{xx} = 2500Sxx=2500 and Sxy=−12S_{xy} = -12Sxy=−12.
Calculate the product moment correlation coefficient (rrr) between the light intensity and the oxygen production rate for these 10 plants.
A researcher claims that plants under higher light intensity significantly increase their oxygen production. Comment on this claim in light of your calculation in part (e).
