Question

Botanists placed seed baits at 5 sites in region A and 6 sites in region B and observed the number of ant species attracted to each site. These data are listed in the table below. Is there evidence to conclude that a difference exists between the average number of ant species found at sites in the two​ regions? Draw the appropriate​ conclusion, using alpha equals 0.05 .

This Question: 10 pts 1 of 4 (0 complete) ► This Test: 50 pts possible Botanists placed seed baits at 5 sites in region A and 6 sites in region B and observed the number of ant species attracted to each site. These data are listed in the table below. Is there evidence to conclude that a difference exists between the average number of ant species found at sites in the two regions? Draw the appropriate conclusion, using a = 0.05. Click the icon to view the table. Let uy be the average number of ant species found in region A and uy be the average number of ant species found in region B. State the null and alternative hypotheses. Number of ant species attracted to each site - X Ho: H1-H2 Hall-H2 Find the test statistic. Site Region Number of Ant Species Site Region Number of Ant Species The test statistic is (Round to two decimal places as needed.) Find the p-value. The p-value is (Round to three decimal places as needed.) Print Done State the conclusion. There is evidence that there is a difference in the average number of ant species found at sites in the two regions. Enter your answer in each of the answer boxes.

Answer 1

The problem is to test that there is difference between the average number of ant species. found at sites in two region. Here first sample is no. of ant species found at sites in the region A and second sample is no of ant species found at sites in the region B let n, be the sum size of sample 1 i.e.n,=5 and nebe the size of sample 2 j.e. 1226 . n, <30 & 2 <30 hence we use t-test for means. Let ell, be the average no. of ant species found in region A and la be the average no. of ant species found to region B.! Hypothesis Horeli ll2 = 0 H, ll, - ll2 to Test statistic t = X.-X2 en Sp I ona where, x = mean of sample 1 = 2x, i 74 = 14.8. ns Te mean of sample 2 = 3 X2 = 73 = 12.1667 12 6 si - Variance of sample 1 EX-X, D 2 - 435, 2 S = Variance of sample 2 = 1 EX2 - 2 n2 121 NA 274.9667

Q Pooled variance nis, 2 th, 82² tha-2 (5) (435.2) & (6)( 274.9667) s+ 6-2 3825. 8 = 425.0889 sp= 425.0889 = 20.6176 Test statistic - t = 14.8 +12.1667 20.61761 s16 .. - 2.6333 12.4885 = 0.2109 P-value is calculated in excel P-value = TOIST (0,2log, g tail =2) = 0.8376 level of significance 2 = 0,05 pse Hence accept Ho conclusion: There is no evidence that there is difference in the average number of ant species found at sites in the two region. jee-420