Question

9. 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.

Answer 1

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.

	r²	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