A magazine listed the number of calories and sodium content (in milligrams) for 13 brands of...
A magazine listed the number of calories and sodium content (in milligrams) for 13 brands of hot dogs. Examine the association, assuming that the data satisfy the conditions for inference. Complete parts a and b.
Variable Coefficient SE(Coeff) t-ratio P-value
Constant 90.4899 83.47 1.08 0.3015
Calories 2.49052 0.5728 4.35 0.0012
a) State the appropriate hypotheses about the slope. Choose the correct answer below.
A. Upper H 0: beta 1 not equals 0; there is a linear association between calories and sodium content. Upper H Subscript Upper A: beta 1 equals 0; there is no linear association between calories and sodium content.
B. Upper H 0: beta 1 equals 0; there is no linear association between calories and sodium content. Upper H Subscript Upper A: beta 1 not equals 0; there is a linear association between calories and sodium content.
C. Upper H 0: beta 1 equals 0; there is no linear association between calories and sodium content. Upper H Subscript Upper A: beta 1 less than 0; there is a negative linear association between calories and sodium content.
D. Upper H 0: beta 1 equals 0; there is no linear association between calories and sodium content. Upper H Subscript Upper A: beta 1 greater than 0; there is a positive linear association between calories and sodium content.
b) Test your hypotheses and state your conclusion in the proper context.
Find the test statistic.
t=____(Round to two decimal places as needed.)
Find the P-value for the test.
The P-value is ____ (Round to four decimal places as needed.)
Fail to reject Reject or Reject the null hypothesis. ____There is sufficient or insufficient evidence____ of a linear association between calories and sodium content in hot dogs.
Homework Answers
a) Null hypothesis
vs
Alternative hypothesis
Option B
b)
t test statistic = 4.35 (by using given output directly )
p value for slope = 0.0012 < 0.05
Therefore we reject H0.
We have sufficient evidence to say that there is linear relationship between calories and sodium content.
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