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 = 0.82 years. However, it is thought that the overall population mean age of coyotes is μ = 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 α = 0.01.

(a) What is the value of the sample test statistic? (Round your answer to three decimal places.)

Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of μ = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 34 waves showed an average wave height of

(b) = 17.2 feet. Previous studies of severe storms indicate that σ = 3.6 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.)

test statistic	=
critical value	=

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 37 arrests last month, 27 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.

(c) What is the value of the sample test statistic? (Round your answer to two decimal places.) and Find the P-value of the test statistic. (Round your answer to four decimal places.)

USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1005 Chevrolet owners and found that 485 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01.

(D) What is the value of the sample test statistic? (Round your answer to two decimal places. AND  Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

• Here we are to test,
  
  
  We use the test statistic:
  
  
  Given Information:
  n = 51
  
  
  
  
  We reject H0 at 1% level of significance, iff
  
  
  The calculated T value is
  
  
  
  Thus, we observe that,
  
  
  Hence, we reject H0 at level 1% and conclude that, the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years.
  
  
  
• Here we are to test,
  
  
  We use the test statistic:
  
  
  Given Information:
  n = 34
  
  
  
  
  We reject H0 at 1% level of significance, iff
  
  
  The calculated T value is
  
  
  
  
  Thus, we observe that,
  
  
  Hence, we fail to reject H0 at level 1% and conclude that, the sample data indicate that this information does not suggest that the storm is (perhaps temporarily) increasing above the severe rating.
  
  
• Here we are to test,
  
  
  We use the test statistic:
  
  
  Given Information:
  n = 37
  
  
  
  We reject H0 at 1% level of significance, iff
  
  
  The calculated T value is
  
  
  
  p-value
  
  
  
  
  
  Hence, we fail to reject H0 at level 1% as the p-value>0.005 and conclude that, the claim that the population proportion of such arrests in Rock Springs is not different from 70%.
  
  
• Here we are to test,
  
  
  We use the test statistic:
  
  
  Given Information:
  n = 1005
  
  
  
  We reject H0 at 1% level of significance, iff
  
  
  The calculated T value is
  
  
  
  p-value
  
  
  
  Hence, we fail to reject H0 at level 1%, as the p-value>0.01 and conclude that, the claim that the population proportion of such arrests in Rock Springs is not different from 70%.
  
  
  

As per Chegg policy, we are supposed to answer the first 3 subparts of the first question. HOwever, I have tried to answer as many questions as I could.

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