A nutrition enthusiast gathered a database on different types of cereals and the

Question

A nutrition enthusiast gathered a database on different types of cereals and their nutritional facts. Among other data in this set, one value given is the National Food Board's overall rating of the cereal. The nutrition enthusiast would like to know if there is a correlation between a cereal's rating and the amount of calories in that cereal.

The test statistic is missing from the output. What is the test statistic for testing the alternative hypothesis that there is a non-zero slope between "calories" and "rating"? Give your answer to 3 decimal places.

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The p-value is also missing from the output. What would be the appropriate range for the missing p-value from the T-table?

Select one:

p-value < 0.01

0.01 < p-value < 0.02

p-value > 0.10

p-value < 0.005

p-value > 0.20

THANKS

Simple linear regression results: Dependent Variable: rating Independent Variable: calories rating 395.788 0.497 calories Sample size 77 Estimate of error standard deviation: 10.243523 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept 95.788 6.550 0 75 14.623 0 75 Slope 0.0603

Explanation / Answer

for estimated slope from regression lineb1=-0.497

hence test stat =b1/std error of slope =-0.497/0.0603=-8.242

degree of freedom =75

for this much degree of freedom and above test stat; p value =0.0000

hence range of p values p-value < 0.005

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