Question

In: Statistics and Probability

The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given...

  1. The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given below. (Source: Consumer Reports)

Calories x

150

170

120

120

90

180

170

140

90

110

Sodium y

420

470

350

360

270

550

530

460

380

330

State the null and alternative hypotheses in symbols and words

H0 =   

Ha =

Calculate the t test statistic. t = _______ Calculate the p-value. _________

Circle the correct conclusion:    Reject H0          or         Fail to reject H0

Explain your conclusion using real-world language – no statistical terms or symbols.

Solutions

Expert Solution

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

t = 6.070

p-value = 0.0003

Reject H0

There is a significant relationship between the caloric contents and the sodium contents of beef hot dogs.

0.822
r   0.906
Std. Error   40.392
n   10
k   1
Dep. Var. y
ANOVA table
Source SS   df   MS F p-value
Regression 60,107.9675 1   60,107.9675 36.84 .0003
Residual 13,052.0325 8   1,631.5041
Total 73,160.0000 9  
Regression output confidence interval
variables coefficients std. error    t (df=8) p-value 95% lower 95% upper
Intercept 80.8130
x 2.4715 0.4072 6.070 .0003 1.5326 3.4105

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