Colored Stones
Statistical Analysis of Colored Stones by using Random Sampling Naomi Malary Lab Report 1 Ecology Lab 312 L-1 October 12, 2009 Introduction Random Sampling, a method often used by ecologist involves an unpredictable component. In this method, all members of the population have an equal chance of being selected as part of the sample. The results involving random sampling can be categorized as descriptive statistics and inferential statistics (Montague 2009).Descriptive statistics includes simplified calculations of a given sample and arrange this information into charts and graphs that are easy to contrast. Trying to reach conclusions that extend beyond the immediate data alone describes inferential statistics. To document the results of sampling, qualitative and quantitative data is used. Quantitative data lack is measured and identified on a numerical scale, whereas Qualitative data approximates data but does not measure characteristics,
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properties and etc. The purpose of this experiment was to use statistical analysis to evaluate random sampling of colored stones (Montague 2009). While conducting this experiment, we came up with a few null hypotheses.
The first null hypothesis is that all the stones that have the same color weigh the same. The second null hypothesis is that there are more blue stones than red or yellow stones. Therefore the Blue stones will be picked the mosr. Our final null hypothesis is that the stones of the same color have the same length and that they will not vary in size. Method Our team was given a box of one hundred and two red, blue, and yellow stones. Team members A and B took turns choosing stones via random sampling, team member E recorded the color of the chosen stone. Team member C measured the weight of the stone with a scale, and team member D measured the length of the stone using a vernier capiler. Team members A and B placed the stones back into the box, mixed it, and we then repeated the procedure. Three sample sets were taken . The first set I were the first 5 samples taken (n=5), set II consist of n=10, and set III consist of n=30.
Results There appeared to be a small difference between stone color and their average weight (Table1. and figures 1-3). Upon observation, you will see that the yellow stones were larger than the blue stones, and the blue stones were larger then the red stones (Table2. and figure 2-3). It can also be noted that the only sample set to have red stones selected was in set III (Figure 3). additionally, figure7 shows that blue stones were picked in greater proportion than the yellow and red stones. Discussion I hypothesized that all stones that share the same color weighs the same. According to table 2, all the stones of the same color do not share the same weight. Though the average seemed relatively the same, there still was a difference in the weight. Therefore, I must reject my null hypothesis on account of this information. The second null hypothesis stated that there are more blue stones than yellow or red stones, therefore more blue stones will be picked than any other stone. According to figure 7, the blue stones accounted for 44%, the yellow stones 38%, and the red stones 18%. Therefore I will not be rejecting my hypothesis on the basis that there were more blue stones present than any other color. The final null hypothesis stated that the stones of the same color have the same length. Table 2 and figures 5-7, accounted for the fact that the yellow stones were usually the longest and the red stones the shortest. Based on this information, I will not be rejecting this null hypothesis. Figure 1: Graph shows the average weight of each colored stone for set=5 Figure 2: Graph shows the average weight of each colored stone for set n=10 Figure3: Graph shows the average weight of each colored stone for set n=30 {draw:frame} {draw:frame} {draw:frame} Figure 4: Graph shows the average weight of each colored stone for set=5 Figure 5: Graph shows the average weight of each colored stone for set n=10 Graph6: Graph shows the average weight of each colored stone for set n=30 {draw:frame} Figure 7: Pie chart shows the total proportion of the stones Reference Montegue, J.M. 2009. BIO 312L: Ecology Lab – Exercise 01 2009. Slides 10,11 Wikipedia, Random Sampling.www.wikipedia.com/random_sample
properties and etc. The purpose of this experiment was to use statistical analysis to evaluate random sampling of colored stones (Montague 2009). While conducting this experiment, we came up with a few null hypotheses.
The first null hypothesis is that all the stones that have the same color weigh the same. The second null hypothesis is that there are more blue stones than red or yellow stones. Therefore the Blue stones will be picked the mosr. Our final null hypothesis is that the stones of the same color have the same length and that they will not vary in size. Method Our team was given a box of one hundred and two red, blue, and yellow stones. Team members A and B took turns choosing stones via random sampling, team member E recorded the color of the chosen stone. Team member C measured the weight of the stone with a scale, and team member D measured the length of the stone using a vernier capiler. Team members A and B placed the stones back into the box, mixed it, and we then repeated the procedure. Three sample sets were taken . The first set I were the first 5 samples taken (n=5), set II consist of n=10, and set III consist of n=30.
Results There appeared to be a small difference between stone color and their average weight (Table1. and figures 1-3). Upon observation, you will see that the yellow stones were larger than the blue stones, and the blue stones were larger then the red stones (Table2. and figure 2-3). It can also be noted that the only sample set to have red stones selected was in set III (Figure 3). additionally, figure7 shows that blue stones were picked in greater proportion than the yellow and red stones. Discussion I hypothesized that all stones that share the same color weighs the same. According to table 2, all the stones of the same color do not share the same weight. Though the average seemed relatively the same, there still was a difference in the weight. Therefore, I must reject my null hypothesis on account of this information. The second null hypothesis stated that there are more blue stones than yellow or red stones, therefore more blue stones will be picked than any other stone. According to figure 7, the blue stones accounted for 44%, the yellow stones 38%, and the red stones 18%. Therefore I will not be rejecting my hypothesis on the basis that there were more blue stones present than any other color. The final null hypothesis stated that the stones of the same color have the same length. Table 2 and figures 5-7, accounted for the fact that the yellow stones were usually the longest and the red stones the shortest. Based on this information, I will not be rejecting this null hypothesis. Figure 1: Graph shows the average weight of each colored stone for set=5 Figure 2: Graph shows the average weight of each colored stone for set n=10 Figure3: Graph shows the average weight of each colored stone for set n=30 {draw:frame} {draw:frame} {draw:frame} Figure 4: Graph shows the average weight of each colored stone for set=5 Figure 5: Graph shows the average weight of each colored stone for set n=10 Graph6: Graph shows the average weight of each colored stone for set n=30 {draw:frame} Figure 7: Pie chart shows the total proportion of the stones Reference Montegue, J.M. 2009. BIO 312L: Ecology Lab – Exercise 01 2009. Slides 10,11 Wikipedia, Random Sampling.www.wikipedia.com/random_sample