d) Compute a 95% confidence interval for the population mean width of all Garrison Bay littleneck clams. (e) How many more littleneck clams would be needed in a sample if you wanted to be 95% sure that the sample mean width is within a maximal margin of error of 10 mm of the population mean width? (f) The same 35 clams were used for measures of length and width. Are the sample measurements length and width independent or dependent? Why?
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Garrison Bay is a small bay in Washington state. A popular recreational activity in the bay is clam digging. For several years, this harvest has been monitored and the size distribution of clams recorded. Data for lengths and widths of littleneck clams (Protothaca staminea) were recorded by a method of systematic sampling in a study done by S. Scherba and V. F. Gallucci"The Application of Systematic Sampling to a Study of lnfaunal Variation in a Soft Substrate Intertidal Environment," Fishery Bulletin, Vol. 74, pp. 937-948). The data in Tables 8-4 and 8-5 give lengths and widths for 35 littleneck clams.
(a) Use a calculator to compute the sample
(b) Compute a 95% confidence interval for the population mean length of all Garrison Bay littleneck clams.
(c) How many more littleneck clams would be needed in a sample if you wanted to be 95% sure that the sample mean length is within a maximal margin of error of 10 mm of the population mean length?
(d) Compute a 95% confidence interval for the population mean width of all Garrison Bay littleneck clams.
(e) How many more littleneck clams would be needed in a sample if you wanted to be 95% sure that the sample mean width is within a maximal margin of error of 10 mm of the population mean width?
(f) The same 35 clams were used for measures of length and width. Are the sample measurements length and width independent or dependent? Why?
The confidence interval is an inference process which is used to estimate the population parameter and gives the
When the
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To compute the sample mean and sample standard deviations follow the steps given below in a calculator.
- Press the key of STAT and go to edit list.
- Enter the data into the list.
- Again press STAT and go to calc option.
- Select VarStat command to compute the sample statistic.
This procedure will give the following sample mean and sample standard deviations for both the samples.
The coefficient of variation is computed by taking the ratio of standard deviation to mean. To find the coefficient of variation of substitute the values of sample means and sample standard deviations in .
So the coefficient of variation for length is 0.22 and for width is 0.233.
As the sample size is more than 30, the confidence interval can be computed using the standard normal distribution. Using the standard normal distribution, the critical value corresponding to 95% confidence level is 1.96.
Substitute the sample size, sample standard deviation of length and critical value in to find the margin of error of length.
To find the 95% confidence interval, substitute the values of sample mean and margin of error in .
So 95% confidence interval for mean length is (406.47, 470.33).
The margin of error is 10, so to compute the sample size substitute critical value 1.96 and estimated sample standard deviation in .
So total required sample size is 357 and 35 observations are already collected, so number of observations that are required collect is .
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