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A random sample of 51 adult coyotes in a region of northernMinnesota showed the average age to be x = 2.05 years,with sample standard deviation s = 0.88 years. However, itis thought that the overall population mean age of coyotes isμ = 1.75. Do the sample data indicate that coyotes in thisregion of northern Minnesota tend to live longer than the averageof 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 = 1.75yr    

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 rationalefor your choice of sampling distribution.

The standard normal, since the sample size is large andσ is known.

The Student's t, since the sample size is large andσ is known.    

The Student's t, since the sample size is large andσ is unknown.

The standard normal, since the sample size is large andσ is unknown.

What is the value of the sample test statistic? (Round your answerto three decimal places.)


(c) Find the P-value. (Round your answer to four decimalplaces.)


Sketch the sampling distribution and show the area corresponding tothe P-value.

(d) Based on your answers in parts (a) to (c), will you rejector fail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.01 level, we reject the null hypothesis andconclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis andconclude the data are not statisticallysignificant.    

At the α = 0.01 level, we fail to reject the null hypothesis andconclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis andconclude the data are not statistically significant.

(e) Interpret your conclusion in the context of theapplication.

There is sufficient evidence at the 0.01 level to conclude thatcoyotes in the specified region tend to live longer than 1.75years.

There is insufficient evidence at the 0.01 level to concludethat coyotes in the specified region tend to live longer than 1.75years.