Question

A gardener plants 300 sunflower seeds (of a brand called KwikGrow) and, after 2 weeks, measures the seedlings’ heights (in mm). These heights are recorded in the file Sunflower.csv. He is interested in testing whether the mean height of sunflowers grown from KwikGrow seeds is greater than 33 mm two weeks after planting.

a. What are the null and alternative hypotheses?

b. (1 mark) What is the value of the test statistic?

c. (1 mark) What is the approximate p-value?

d. Which assumption is required for the p-value in c) to be valid?

e. Using a significance level of = 0.05, state your conclusions in the language of the problem.

file=

height

38.6, 39.1, 50.4, 49.2, 46.2, 0, 43.1, 49.6, 16.1, 17.9, 11.6, 50.2, 36.5, 50.6, 40.3, 36.3, 14.3, 40.8, 12.1, 43.7, 47.2, 49.9, 37.9, 49.1, 53, 47.7, 13.8, 38.3, 49.2, 50.6, 49.6, 52.3, 19.8, 12.8, 46.9, 35.3, 38.7, 39.3, 12.4, 51.9, 36.9, 20.8, 51.7, 38.8, 41.9, 18.4, 41.4, 48.7, 16.3, 50, 13.8, 50.3, 47.6, 42, 14.9, 41.1, 43.7, 10.1, 36.4, 40.1, 14.9, 50.3, 12.3, 44.3, 49.1, 10.7, 14.9, 48.2, 14.8, 38, 41.4, 39.4, 11.9, 13.8, 0, 35.1, 37.3, 47.5, 12.5, 11.8, 16, 15.7, 38.1, 58.6, 51.2, 37.4, 36.4, 40.8, 35.2, 15.5, 55.9, 42.1, 47.9, 41.1, 38.5, 51.1, 41, 53.8, 41.5, 38.6, 48, 50.4, 17.9, 50.8, 39.2, 13.5, 35.9, 12.4, 16.5, 47.9, 38.4, 11.7, 49.4, 44.7, 45.8, 14, 40.4, 48.9, 44.6, 17.6, 12.4, 43.1, 18.3, 20, 17.1, 50.1, 57.6, 50.9, 50.2, 18.3, 0, 14.5, 40, 49.3, 51.9, 16.1, 47, 14.6, 48.7, 38.1, 39.7, 39.3, 0, 37.1, 13, 17.4, 37.7, 41.3, 39.6, 18, 17.4, 38.3, 48.9, 54.9, 41.5, 13.8, 36.6, 56.7, 35.6, 42.4, 0, 49.7, 11, 17.1, 47.4, 17.1, 14.2, 43.3, 52.4, 14.4, 18.7, 16.7, 50.9, 15.2, 12.4, 14.6, 43.5, 46.8, 45.6, 42, 49.8, 50.4, 51.5, 14.7, 50.9, 15, 34.8, 52.3, 35.5, 13.6, 44.6, 14.1, 47.5, 16.3, 40.9, 52.6, 44, 49.8, 0, 40.3, 50.9, 18.6, 56.9, 40.1, 49.3, 45, 0, 38.7, 14.4, 15.2, 48.9, 53.6, 42.6, 14.6, 39, 49.5, 42.3, 54.5, 12.5, 14.2, 51.5, 41, 12.3, 51.2, 43.2, 17.8, 34.8, 50.1, 53, 53.1, 13.4, 16.5, 17.7, 45, 39.2, 47.2, 37.9, 45.6, 7.6, 49.4, 48.7, 40.2, 15.6, 50.5, 48.2, 0, 41.8, 45.6, 40.9, 38.2, 0, 52.1, 9.3, 17.9, 36.8, 39.6, 11.3, 48.5, 55.6, 38.1, 37.8, 52.4, 40.5, 46.5, 38.7, 15.4, 53.1, 20.8, 49.2, 49.5, 42.6, 10.1, 45.8, 42.6, 42.2, 36.5, 45.2, 41.5, 43.3, 39.9, 17.1, 15.7, 32.9, 40.8, 38.5, 39.8, 52.2, 15.9, 13.6, 20.7, 44, 13.7, 0, 50, 13.6, 38.7, 51.5, 16.4, 37.2, 15.1

Answer 1

a) null hypothesis :-  the mean height of sunflowers grown from KwikGrow seeds is not greater than 33 mm two weeks after planting.

alternative hypothesis :-  the mean height of sunflowers grown from KwikGrow seeds is greater than 33 mm two weeks after planting.

we find the result of the problem by using r software as,

i) copy the given 300 data and paste in r as

=>data = c( paste)

=>data

=>result=t.test(data)

=>result

then we get , as follows given by r code excuted

b) the value of the test statistic t = 37.58

c)  the approximate p-value = 2.2e-16

d) assumption is required for the p-value in c) to be valid is that,

i) if p value > 0.05 accept null hypothesis

ii) if p value < 0.05 reject null hypothesis

Result :- p value( 2.2e-16) < 0.05 reject null hypothesis i.e. accept alternative hypothesis.

Conclusion :- for the significance level of 0.05, the mean height of sunflowers grown from KwikGrow seeds is greater than 33 mm two weeks after planting.