The Wisconsin Fast Plant (Brassica campestris) has a very rapid growth cycle tha

Question

The Wisconsin Fast Plant (Brassica campestris) has a very rapid growth cycle that makes it particularly well-suited for studying factors that affect plant growth. A random sample of plants was treated with the substance Ancymidol and compared a control group of plants that was given ordinary water. The heights of all of the plants were measured (in cm) after two weeks of growth: 14.3 Ancymidol Control 7.7 19.2 12.8 14.3 5.5 21.2 19.0 9.2 13.1 20.4 8.2 19.7 Conduct the appropriate test to determine if there is a difference in plant height after two weeks of growth if plants were given Angymidol compared to water. Include all steps for full credit. (2.5pt)

Explanation / Answer

Here we will use the t test for equal variances.

H0 : There s no difference in plant height after two weeks of growth if plants were given ancymidol compared to water. ?1 = ?2

Ha : There is significant difference in plant height after two weeks of growth if plants were given ancymidole compared to water. ?1 ?  ?2

Significance level alpha = 0.05

Summary for two given sample

sample mean for plant growth for control group x?2 = 17.333

sample standard deviation for plant growth for control group s2 = 4.665

sample mean for plant growth for ancymidol group x?1 = 11.514

sample standard deviation for plant growth ffor ancymidol group s1 = 4.6488

Pooled standard deviation sp = = sqrt [{(n1 -1)s12 + (n2 -1)s22}/(n1 +n2?-2)]

sp = sqrt[(6 * 21.6114 + 5 * 21.7587)/(6 + 5) ] = 4.656

standard error of sample difference sed = sp * sqrt (1/n1 + 1/n2) = 4.656 * sqrt(1/7 + 1/6) = 2.59

Test statistic

t = (x?1 -x?2)/ sed = (17.333 - 11.5143)/2.59 = 2.2466

Here dF = 7 + 6 - 2 = 11 and alpha = 0.05 and two tailed test

tcritical = 2.20

so here t > tcritical so we will reject the null hypothesis and can conclude that There is significant difference in plant height after two weeks of growth if plants were given ancymidole compared to water.

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