Question

A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x 2.01 years, with sample standard deviations 0.72 years. However, it is thought that the overall population mean age of coyotes is u = 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 O HO! 1.75 yr: H 1.75 y O HOM> 1.75 yr: H 1.75 y O Ho! < 1.75 yr: H = 1.75 y O Ho: 1.75 yr: Hy!< 1.75 y O MO! 1.75 yr; H> 1.75 y (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution The Student'st, since the sample size is large and is unknown The standard normal, since the sample size is large and is unknown The standard normal, since the sample size is large and is known 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.)

Answer 1

Given n=46, xbar=2.01, s=0.72, mean=1.75

a) level of significance

$\alpha$=0.01

The test hypothesis is

Null and alternative hypothesis are
Ho:μ=1.75
Ha:μ>1.75

b:sampling distribution is

the student t sice sample size is large and $\sigma$ is unknown

#Sample test statistics

t=(xbar-μ)/(s/√n)

=(2.01-1.75)/(0.72/sqrt(46))

t= 2.45

test statistics=2.45