Question

A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.84 years. However, it is thought that the overall population mean age of coyotes is μ = 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 α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 1.75 yr; H1: μ ≠ 1.75 yr H0: μ < 1.75 yr; H1: μ = 1.75 yr H0: μ > 1.75 yr; H1: μ = 1.75 yr H0: μ = 1.75 yr; H1: μ > 1.75 yr H0: μ = 1.75 yr; H1: μ < 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 σ is unknown. The Student's t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and σ is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.

Answer 1

solution:

sample size = n= 46

sample standard deviation = S = 0.84

sample mean = = 2.05

we have to test that the coyotes tend to live longer than average of 1.75 years.

a) level of significance = = 0.01

degree of freedom = 46-1 = 45

b) null and alternative hypothesis:

it is a right tailed test

we will use the student's t-distribution since, sample size is large and sigma is unknown

test statistics:

p value = 0.0098

since p value < 0.01, so reject the null hypothesis

conclusion:

there is enough evidence to support the claim that mean life of coyotes is greater than 1.75 years