Widths of Littleneck Clams (mm) in Garrison Bay
By: Brooke and Olivia
In our study, we had to analyze the widths of Littleneck Clams in Garrison Bay. These clams are also called quahog. They are the smallest type of clam around, averaging from 7 to 10 clams per pound. These Littleneck clams can be found in on most sea/ocean shorelines from California to places in Maine. The data we have is from waters in Washington State.
We took a sample of Littleneck clams, because it would be impossible to figure out the lengths of every single clam in the waters. Our sample size was 35 clams, that is a very small portion of the population, but it is large enough for everything we are finding. We had to find the sample mean, sample standard deviation, degrees of freedom, critical values for different confidence levels, margin of error we could have, and the confidence interval for the population mean.
The sample mean was calculated by using google sheets. We determined that the average width of Littleneck clams was 83.62 mm. We also calculated the sample standard deviation by using google sheets. This number shows you how spread out your data is from the mean. Our sample standard deviation was 89.38 mm, which means that the widths of the clams varied greatly and is very spread out. We had a couple extremely small clams and a couple extremely large clams. Our degree of freedom was 34 clams, you take the sample size and subtract one. Degrees of freedom tells you how much your data can vary.
We also had to deal with confidence levels, which is the probability that that percent of the data will fall between certain intervals of the data. There are many different ways you can determine the confidence level intervals, it all depends on if you have a sample or population and if you know or not. For us we had to use the formula for when is unknown, which also caused us to use the larger table. The confidence levels, 90%, 95%, and 99% were all used to find the margin of error and the confidence intervals for the population mean. In order to start finding these calculations out, we had to find Tc using the table. Then plugging in the information that we knew into the different equations.(see calculations below). The next thing we had to do was find the margin of error. The margin of error shows an amount that is allowed for miscalculations and mistakes(see calculations below). The last thing we had to find was the confidence intervals for each confidence level. This means that there is a % confidence that the width of the clams will be between those two numbers(see calculations below). With a 90% confidence level, we can say that the population mean for the width of Littleneck clams is between 358.10mm and 409.14 mm. With a 95% confidence level, we can say that the population mean for the width of Littleneck clams is between 352.95mm and 414.3mm. Then lastly with a 99% confidence level, we can say that the population mean for the width of Littleneck clams is between 342.47mm and 424.78mm.
If we would have been given , all of our calculations, equations, and answers would have been different.
Calculations:
Sample size: how many numbers we worked with= 35 clams
Sample mean: calculated by using google sheet= 83.62 mm
Sample standard deviation: calculated using google sheet= 89.38mm
Degrees of freedom: 35-1=34 clams
Critical values for 90%, 95%, and 99% confidence levels
To get Tc, look at table 4, find confidence level at told and go to sample size on the side
c=.9 tc=1.69 c=.95 tc=2.03 c=.99 tc=2.72
Maximal margin of error for 90%, 95%, and 99% confidence levels
E=Tc x (s/√n)
c=.9 E= 25.51 c=.95 E= 30.67 c=.99 E=41.15
Determine 90%, 95%, and 99% confidence intervals for (the population mean)
X-E< < X+E
358.10<<409.14 352.95<<414.3 342.47<<424.78