1. 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 little neck 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 Infaunal Variation in a Soft Substrate Intertidal Environment,” Fishery Bulletin, Vol. 74, pp. 937–948). The data in Tables 7-4 and 7-5 give lengths and widths for 35 little neck clams.

(a) Use a calculator to compute the sample mean and sample standard deviation for the lengths and widths. Compute the coefficient of variation for each.

(b) Compute a 95% confidence interval for the population mean length of all Garrison Bay little neck clams.

(c) How many more little neck 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?

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(d) Compute a 95% confidence interval for the population mean width of all Garrison Bay little neck clams.

(e) How many more little neck 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?