4. (Three parts; 10 marks in total) Conservation biologists stationed in St. Joh

Question

4. (Three parts; 10 marks in total) Conservation biologists stationed in St. John's, Newfoundland have been researching the lifespan of local avian wildlife. Specifically, they have recently focused on puffins. A recent random sample of 8 puffins gave a standard deviation of 1.715 and a confidence interval of (6.826, 8.542) Assume that the assumptions are met for the required analysis. (a) (4 marks) Determine the confidence level of this interval. (b) (4 marks) Find a 98% confidence interval for the mean lifespan of all puffins in St. John's SHOW ALL STEP S) (c) (2 marks) A previous research study claims that the average lifespan of puffins is 6.5 years. Based on the confidence interval given in the question (6.826, 8.542), evaluate whether this claim is true. Also, based on the 98% confidence interval you calculated in part (b), evaluate whether this claim is true. Did these two confidence intervals give you the same evaluation? Explain why or why not

Explanation / Answer

a) confidence interval = (Xbar - t * s/sqrt(n)) , (Xbar +t * s/sqrt(n)) ,

Xbar - t * 1.715 /sqrt(8) = 6.826

Xbar + t * 1.715 /sqrt(8) = 8.542

hence

Xbar = (6.826 + 8.542)/2 = 7.684

t = (8.542 - 7.684)/(1.715 /sqrt(8) )

= 1.415

df = 8-1=7

2 P( t > 1.415) = =T.DIST.2T(1.415,7)=0.2

hence confidence interval = 1-0.2 = 80%

b)

98 %

t = 2.99795

CI = (5.866, 9.502)

c) since 6.5 is not in 80% confidence interval , we reject the null hypothesis at 20% significance level

6.5 is present in 98 % confidence interval . we fail to reject the null at 2 % level of significance

No, both confidence level give different result

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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