A random sample of 45 adult coyotes in a region of Minnesota showed the average

Question

A random sample of 45 adult coyotes in a region of Minnesota showed the average age to be x = 1.99 years, with sample standard deviation of 0.90 years. However, it is thought that the overall population mean age of coyotes is approximately 1.75. Does the data indicate that coyotes in the sampled region of Minnesota tend to live longer than the average of 1.75 years? Use = 0.01. (a) Identify the claim, the null hypothesis, and the alternative hypothesis. Claim: 1.75 Ho: 1.75 H1: 1.75 (b) Will you use a left-tailed, right-tailed, or two-tailed test? two-tailed left-tailed right-tailed (c) 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 Student's t, since we assume that x has a normal distribution and is known. The Student's t, since the sample size is large and is known. The Student's t, since we assume that x has a normal distribution and is unknown. The standard normal, since the sample size is large and is unknown. (d) Sketch the sampling distribution showing the area corresponding to the approximate P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (e) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (f) State your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years. Fail to reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years. Reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years. Reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years.

Explanation / Answer

a) Random sample, n=45, Sample mean = 1.99, Same dev = 0.9, Pop. Mean = 1.75

To test if theyCoyotes in this region live longer than 1.75, we have Test Design as:

a)

Claim: 1.75 Ho: 1.75 H1: 1.75

H0: The Coyote in this region do not live longer than 1.75 years

Ha: The Cotyotes in this region live longer than 1.75 years

b) Use a right tail test becasue 1.99 ( sample mean) > 1.75( pop. mean ). Therefore this sample lies to the right of the Mean of Normal Dist( which is the pop. mean of 1.75). So to test if sample is too high than 1.75, we have to test the number of Std. Devs this sample is from Pop. mean.

t = (1.99 - 1.75)/(0.9/sqrt(45)) = 1.78.

Corresponding P value with t=1.78 and Df= n-1=44. we have , P=0.9590( Please refer T tables with these Params)

Since Alpa=0.01 we have this area inside 1-0.01 = 0.99. Thefore, the 1.99 sample mean is not significantly Difference. Hence we failed to reject the Null Hypothesis (H0):The Coyote in this region do not live longer than 1.75 years.

c) We use the t dist because the sample and Pop means are known, dist is Normal , but Pop. Std dev ( Sigma) is unknown.

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