STA 2014 Statistics Week 12, Individual Work 6 solution correct answers

STA 2014 Statistics Week 12, Individual Work 6 solution correct answers

Continue to practice working with hypothesis testing in your Individual Work assignment.

Please complete the problems from Chapters 10 and 4 listed below.

Section 10.1 - numbers 18, 26

Section 10.2 - numbers 22a-c*, 22c**

Section 10.3 - numbers 8, 10

Section 4.1 - numbers 24a , 10, 14, 24c-d

*Use classical approach; **use P-Value approach.

Section 4.1  Skill Building

In problems 9-12, determine whether the scatter diagram indicates that a linear relation may exist between the two variables.  If the relation is linear, determine whether it indicates a positive or negative association between the variables.

10. see image in text book.

14. Match the linear correlation coefficient to the scatter diagram.  The scales on the x- and y- axes are the same for each scatter diagram.

(a) r = -0.969

 (b) r = -0.049

 (c) r = -1

 (d) r =-0.992

24. American black bears, The American black bear is one of eight bear species in the world.  It is the smallest North American bear and the most common bear species on the planet.  In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park.  One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field).  One variable thought to be related to weight is the length of the bear.  The following data represents the lengths and weights of 12 American black bears.

(a) Which variable is the explanatory variable based on the goals of the research?

 (c) Determine the linear correlation coefficient between weight and height?

 (d) Does a linear relation exist between the weight of the bear and its height/

10.1 Skill Building

18. Fair Packaging and Labeling, Federal law requires that a jar of peanut butter that is labeled as containing 32 ounces must contain at least 32 ounces.  A consumer advocate feels that a certain peanut butter manufacturer is shorting customers by under filling the jars.

In problems 23-34, state the conclusion based on the results of the test.

26. For the hypotheses in Problem 18, the null hypothesis is rejected.

10.2 Applying the Concepts

22.  SAT Exam Scores, A school administrator wonders if students whose first language is not English score differently on the math portion of the SAT exam than students whose first language is English.  The mean SAT math score of students whose first language is English is 516, on the basis of data obtained from College Board.  A simple random sample of 20 students whose first language is not English results in sample mean SAT math score population standard deviation of 114.

(a) Why is it necessary for SAT math scores to be normally distributed to test the hypotheses using the methods of the section?

 (c) Use the classical or P-value approach at the a = 0.1 level of significance to test the hypothesis in part (b).

10.3 Skill Building

8. To test Hₒ:µ = 80 versus H1:µ˂80. A simple random sample of size n=22 is obtained from a population that is known to be normally distributed.

(a) If = 76.9 and s = 8.5, compute the test statistic.

 (b) If the researcher decides to test this hypothesis at the a = 0.02 level of significance, determine the critical value.