A random sample of 51 adult coyotes in a region of northern Minnesota showed the

Question

A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.80 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? For a question such as this I am able to find the value of the sample test statistic but I cannot figure out how to find the P value, Could someone thoroughly explain how to find it?

Explanation / Answer

as n = 51 therefore we will use the z table

null hypothesis = H0 = U = 1.75

ALTERNATE HYPOTHESIS = Ha = u >1.75

a) significance level = 0.01

is will be a right tail test

the critical region = z >2.33

test static = (x-mean)/standard deviation/sqrt(n)

= (2.03 -1.75)/ (0.8/sqrt(51))

= 2.5

as the z= 2.5>2.33 therefore we will reject the null hypothesis

p value = 0.0062 from the z table.

p value = 1 - p(z= 2.5)

= 1 - 0.9938 = 0.0062

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