Table 1: Fish caught per day, by time period and fish attractors. Time Periods P

Question

Table 1: Fish caught per day, by time period and fish attractors.

Time Periods Pipe
1 6.64 9.73

2 7.89 8.21 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 0.52 13 4.86 5.38 14 1.80 2.33 15 0.23 0.91 16 0.58 0.79

(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

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.

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 27.898.21 3 1.83 2.17 0.42 0.75 5 0.85 1.61 6 0.290.75 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 0.52 13 4.865.38 14 1.80 2.33 15 0.23 0.91 16 0.58 0.79 (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

Here,n=sample size=16

(a) Paired t test-

R-command-

t.test(x, y ,paired =T,conf.level=0.99)

Output-

Paired t-test

data: x and y
t = -3.0496, df = 15, p-value = 0.00811
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-1.07038573 -0.01836427
sample estimates:
mean of the differences
-0.544375

Conclusion:Since p-value = 0.00811>0.01 , one attractor is more effective than other.

(b) (i) Assuming equal variance :

R-command is-

t.test(x, y , alternative = "two.sided", mu = 0, paired = FALSE, var.equal =TRUE, conf.level = 0.99)

Output-

Two Sample t-test

data: x and y
t = -0.56979, df = 30, p-value = 0.5731
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-3.171716 2.082966
sample estimates:
mean of x mean of y
1.711875 2.256250

Conclusion:Since p-value = 0.5731<0.01,the average number of fish caught per fishing day by two types of fish attractors, one made from vitrified clay pipes, and the other from cement blocks and brush are same.

(ii) Assuming uneual variance-

R-cammand-

t.test(x, y, alternative = "two.sided", mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.99)

Output-

Welch Two Sample t-test

data: x and y
t = -0.56979, df = 29.251, p-value = 0.5732
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-3.176247 2.087497
sample estimates:
mean of x mean of y
1.711875 2.256250

Conclusion:Since p-value =   0.5732<0.01,the average number of fish caught per fishing day by two types of fish attractors, one made from vitrified clay pipes, and the other from cement blocks and brush are same.

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