Question

A random sample of 46 adult coyotes in a region of northem Minnesota showed the average age to be x - 2.07 years, with sample standard deviations - 0.88 years. However, it is thought that the overall population mean age of coyotesis - 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a -0.01. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: -1.75 yr; H: > 1.75 yr Ho: < 1.75 yr; H = 1.75 yr Ho: -1.75 yr; M: < 1.75 yr Hou - 1.75 yr; H: * 1.75 yr Ho: > 1.75 yr; -1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution The Student's t, since the sample size is large and is unknown The standard normal, since the sample size is large and is known The standard normal, since the sample size is large and is unknown The Student's t, since the sample size is large and is known What is the value of the sample test statistic? (Round your answer to three decimal places) te Estimate the value

Answer 1

Answer:

Given,

alpha = 0.01

Ho : u <= 1.75

Ha : u > 1.75

test statistic z = (x -u)/(s/sqrt(n))

substitute values

= (2.07 - 1.75)/(0.88/sqrt(46))

= 2.47

P value = P(z > 2.47)

= 0.0067557 [since from z table]

= 0.0068

Here we observe that, p value < alpha, so we reject Ho.

So there is sufficient evidence to support the claim.