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 u = 1.75. Do data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Ο F μE 1.75 Yr; H μ> 1.75 yr Ο F μ= 1.75 Yr; H με 1.75 γr O Ho: H = 1.75 yr; Hại µ < 1.75 yr O Ho: H < 1.75 yr; H: # = 1.75 yr Ο F μ .75 y H μ= 1.75 γr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.250 O 0.100 < P-value <0.250 O 0.050 < Pvalue <0.100
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 u = 1.75. Do data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Ο F μE 1.75 Yr; H μ> 1.75 yr Ο F μ= 1.75 Yr; H με 1.75 γr O Ho: H = 1.75 yr; Hại µ < 1.75 yr O Ho: H < 1.75 yr; H: # = 1.75 yr Ο F μ .75 y H μ= 1.75 γr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.250 O 0.100 < P-value <0.250 O 0.050 < Pvalue <0.100
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
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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.
I need help with sketching (d) and (e)
Transcribed Image Text: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 u = 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 a = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: µ = 1.75 yr; H: µ > 1.75 yr
Ο H0: μ= 1.75 yr; Η : μ + 1.75 yr
О но: и 3 1.75 уг; н,: и < 1.75 yr
О но: и < 1.75 уг; H;: и 3D1.75 yr
Ο H0: μ > 1.75 yr; H,: μ = 1.75 yr
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since the sample size is large and o is known.
O The standard normal, since the sample size is large and o is unknown.
O The Student's t, since the sample size is large and o is unknown.
O The Student's t, since the sample size is large and o is known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate the P-value.
O P-value > 0.250
0.100 < P-value < 0.250
O 0.050 < p-value < 0.100
O 0.010 < P-value < 0.050
O p-value < 0.010
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value.
a
b
-4
-2
4
-4
-2
2
4
d
-4
-2
4
-4
-2
(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?
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 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.
O 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.
O 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.
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