Question

C is for cabbage ~ A researcher wants to know if the head weight of the cabbage is a good predictor for ascorbic acid (vitamin C) content. From a random sample of 60 cabbages, the researcher recorded the ascorbic acid content in milligrams and the weight of the cabbage head in pounds.
Head weight is the X variable and Ascorbic acid content is the Y variable in this scenario.

R output Coefficients:                Estimate       Std. Error     t value        Pr(>|t|)    (Intercept)    77.574         3.096         25.052        < 2e-16 *** HeadWeight     -7.567         1.131         -6.689         9.75e-09 *** --- Residual standard error: 7.668 on 58 degrees of freedom Multiple R-squared: 0.4355, Adjusted R-squared: 0.4257 F-statistic: 44.74 on 1 and 58 DF, p-value: 9.753e-09

What are the null and alternative hypotheses to test if there is a linear relationship between the X variable and the Y variable in this scenario?

Question 13 options:

1234 Alternative hypotheses 1234 Null Hypotheses

1. β1 = 0 2. b1 = −7.567 3. β1 ≠ 0 4. b1 ≠ −7.567

Answer 1

Solution :

From the given output ,

Null Hypotheses : β1 = 0

Alternative hypotheses : β1 ≠ 0