A random sample of 41 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.07 years, with sample standard deviations = 0.82 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?
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State the null and alternate hypotheses.
A-H
0: ? = 1.75 yr;H
1: ? ≠ 1.75 yr
B-H
0: ? > 1.75 yr;H
1: ? = 1.75 yr
C-H
0: ? = 1.75 yr;H
1: ? > 1.75 yr
D-H
0: ? < 1.75="">H
1: ? = 1.75 yr
E-H
0: ? = 1.75 yr;H
1: ? < 1.75="">
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
A-The Student'st, since the sample size is large and ? is unknown.
B-The Student'st, since the sample size is large and ? is known.
C-The standard normal, since the sample size is large and ? is unknown.
D-The standard normal, 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.)
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(c) Estimate theP-value.
A-P-value > 0.250
B-0.100 P-value <>
C-0.050 P-value <>
D-0.010 P-value <>
E-P-value <>
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
A-At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
B-At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.C-
At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
D-At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
A-There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.
B-There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.