Question

Flowering shrubs in the genus rhododendron have an average height of 57 inches. A team of botanists tests whether rhododendrons’ heights will change if exposed to overwatering. Generally, rhododendrons should receive one inch of water per day; instead, these botanists gave 14 rhododendrons three inches of water per day for three years. These 14 rhododendrons reached an average height of 42 inches with a variance of 463.11.

A. What is μ? If it is not reported, answer “N/A”.
B. What is σ? If it is not provided, answer “N/A”.
C. What sample means are provided? If this is a within-subjects design, include D̄ as well as x̄.
D. What are the s values? If this is a within-subjects design, report s for each condition as well as sD.
E. What is N? If this is a between-subjects design, report n1 and n2 in addition to N.
F. What are the degrees of freedom?
G. Is this a one- or two-tailed test?
H. What is the null hypothesis (H0)?
I. What is the alternative hypothesis (Ha)?
J. What inferential test should be used here? (Note that the options are a z test, a one-sample t test, an independent-samples t test, or a related- samples t test.)

K. What is the standard error? Depending on what kind of inferential test is being used, this will be σx̄, sx̄, sx̄1−x̄2, or sD̄.
L. What is zcrit or tcrit? (Obviously, this depends on whether this question calls for a z or t test.)
M. What is your obtained test statistic (i.e., what is zobt or tobt)?
N. Given the obtained and critical values, what is the appropriate conclusion to draw?

Answer 1

(A)

57

(B)

N/A

(C)

42

(D)

s =

463.11 = 21.52

(E)

14

(F)

Degrees of freedom = n - 1 = 14 -1 = 13

(G)

two - tailed

(H)

H0:Null Hypothesis: $\mu$ = 57

(I)

Ha: Alternative Hypothesis: $\mu \neq$ 57

(J)

one-sample t test

(K)

Standard Error is given by:

Si =- 21.52 V14 = 5.7515

(L)
t_crit = $\pm$ 2.1604

(M)

t_obt = (42 - 57)/5.7515

= - 2.6080

(n)

Since calculated value of t = - 2.6080 is less than critical value of t= - 2.1604, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that rhododendrons’ heights will change if exposed to overwatering.