5. Two types of fish attractors, one made from vitrified clay pipes, and the oth

Question

5. Two types of fish attractors, one made from vitrified clay pipes, and the other from cement blocks and brush, were used during 16 different time periods spanning four years at Lake Tohopekaliga, Florida. The following observations are of the average number of fish caught per fishing day Table 1: Fish caught per day, by time period and fish attractors. Time Periods Pipe Brush 1 6.64 9.73 2 7.898.21 3 1.83 2.17 4 0.42 0.75 5 0.85 1.61 6 0.29 0.75 7 0.57 0.83 8 0.63 0.56 9 0.32 0.76 10 0.37 0.32 11 0.00 0.48 12 0.11 0.5 13 4.86 5.38 14 1.80 2.3:3 15 0.23 0.91 16 0.58 0.7 (a) Use the R t.test ) function to do a paired t-test to determine whether or not one attractor is more effective. Use level 0.01 (b) Repeat part (a), but assume the samples are independent. Use procedures for both equal and unequal variances. Does your conclusion change?

Explanation / Answer

R code:

# t test

pipe <- c(6.64,7.89,1.83,0.42,0.85,0.29,0.57,0.63,0.32,0.37,0.0,0.11,4.86,1.80,0.23,0.58)

brush <- c(9.73,8.21,2.17,0.75,1.61,0.75,0.83,0.56,0.76,0.32,0.48,0.52,5.38,2.33,0.91,0.79)

t.test(pipe,brush,paired = TRUE)

t.test(pipe,brush,alternative = "two.sided", var.equal = TRUE, conf.level=.95)

t.test(pipe,brush,alternative = "two.sided", var.equal = FALSE, conf.level=.95)

R output:

t.test(pipe,brush,paired = TRUE)

        Paired t-test

data: pipe and brush

t = -3.0496, df = 15, p-value = 0.00811

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-0.924855 -0.163895

sample estimates:

mean of the differences

              -0.544375

> t.test(pipe,brush,alternative = "two.sided", var.equal = TRUE, conf.level=.95)

        Two Sample t-test

data: pipe and brush

t = -0.56979, df = 30, p-value = 0.5731

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-2.495559 1.406809

sample estimates:

mean of x mean of y

1.711875 2.256250

> t.test(pipe,brush,alternative = "two.sided", var.equal = FALSE, conf.level=.95)

        Welch Two Sample t-test

data: pipe and brush

t = -0.56979, df = 29.251, p-value = 0.5732

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-2.497656 1.408906

sample estimates:

mean of x mean of y

1.711875 2.256250

Paired t result,

t = -3.0496, df = 15, p-value = 0.00811 which is < 0.05 level. The difference is significant.

Independent t test with equal variance,

t = -0.56979, df = 30, p-value = 0.5731. The difference is not significant.

Independent t test with un equal variance,

t = -0.56979, df = 29.251, p-value = 0.5732. The difference is not significant.

Both equal and unequal variance tests produce similar result.

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