A random sample of 46 adult coyotes in a region of northern Minnesota showed the

Question

A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.78 years. However, it is thought that the overall population mean age of coyotes is ? = 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 ? = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: ? < 1.75 yr; H1: ? = 1.75 yrH0: ? = 1.75 yr; H1: ? ? 1.75 yr    H0: ? > 1.75 yr; H1: ? = 1.75 yrH0: ? = 1.75 yr; H1: ? > 1.75 yrH0: ? = 1.75 yr; H1: ? < 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

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.    The Student's t, since the sample size is large and ? is unknown.The standard normal, since the sample size is large and ? is unknown.

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.)

A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.78 years. However, it is thought that the overall population mean age of coyotes is ? = 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 ? = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: ? 1.75 yr; H1: ? 1.75 yr O Ho: ?-1.75 yr, H1: ? > 1.75 yr C Ho: ?-1.75 yr, H1: ?

Explanation / Answer

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H0 : ? = 1.75
HA : ? > 1.75

Hypothesis test results:

Hence,

a) Level of significance = 0.01

Hypotheses: H0: ? = 1.75 yr; H1: ? > 1.75 yr

b) The Student's t, since the sample size is large and ? is unknown.

Test statistic = 2.435

c) P - value = 0.0095

Mean Sample Mean Std. Err. DF T-Stat P-value ? 2.03 0.11500473 45 2.4346826 0.0095

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