a cactiA 1 square km plot of land near Tucson, AZ (b) What is the explanatory va

Question

a cactiA 1 square km plot of land near Tucson, AZ    

(b) What is the explanatory variable and what type of variable is it?

Year, numericalYear, categorical    Number of cacti in a plot, numericalNumber of cacti in a plot, categorical

(c) What is the response variable and what type of variable is it?

Year, numericalYear, categorical    Number of cacti in a plot, numericalNumber of cacti in a plot, categorical

(d) Which type of test is most appropriate?

Independent Samples t test because each subject (a cactus) had its response measured only once and there was no matching.Paired samples t test because each subject (plot of land) had its response (# of cactus) measured twice, once in 1970 and again in 2001.    Either test is appropriate.

(e) If you were to do a Paired T Test of the claim that the typical number of cacti per square km in Tucson, AZ in the year 2001 is less than the typical number of cacti per square km in Tucson, AZ in the year 1970, what would your hypotheses be?

H0: d = 0 and Ha: d < 0 where d = mean difference in number of cacti per square km (2001 - 1970)H0: d = 0 and Ha: d > 0 where d = mean difference in number of cacti per square km (2001 - 1970)    H0: 2001 - 1970 = 0 and Ha: 2001 - 1970 > 0

(f) Are the conditions satisfied for this test?

NoYes    

(g) What is the p-value of the test?
(Use 4 decimal places)

(h) What is your decision at the = 0.05 level?

Reject the null because the p-value is less than alpha.Fail to reject the null because the p-value is less than alpha.    Reject the null because the p-value is greater than alpha.Fail to reject the null because the p-value is greater than alpha.

(i) Complete the conclusion statement below.

"There  statistical evidence at the  significance level that the average number of cacti per square km in 2001 in Tucson, AZ is less than the average number of cacti per square km in 1970 in Tucson, AZ."

Distributions of the difference 1.64 0.97 3 1.28 0.9 0.8 0.67. 0.0- 0.5 E -0.67 0.2 1.2 E 0.1 -1.64U 0.03 8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 Matched Pairs Difference: in 2001 in 1970 in 2001 680.6 t-Ratio 3.57246 683.333 DF in 1970 14 Mean Difference 2.7333 Prob It 0.0031 0.76511 Prob t 0.9985 Std Error Upper 95% 1.0923 Prob t 0.0015 -4.3743 Lower 95% 15 Correlation 0.99981

Explanation / Answer

Solution:-

a) 1 square km plot of land Tucson, AZ is the subject in this study.

b) Year, categorical , is the explanatory variable.

c) Number of cacti in a plot, numerical is the response variable.

d) Paired samples t test because each subject had its response measured twice, once in 1970 and again in 2001.  

e) H0: d = 0 and Ha: d < 0 where d = mean difference in number of cacti per square km (2001 - 1970)

f) Yes

g) The p-value of the test is 0.0015,s ince this is one tailed test.

h) Reject the null because the p-value is less than alpha.

i) There is sufficient statistical evidence at the  significance level 0.05, that the average number of cacti per square km in 2001 in Tucson, AZ is less than the average number of cacti per square km in 1970 in Tucson, AZ.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.