Hypothesis Testing using dichotomous and 7-point Likert scale

Question

I am working on testing the following hypothesis:

H1: People who are worried about their health will consume yogurt H0: People who are worried about their health will not consume yogurt

I have interviewed 46 respondents using a 7-point Likert scale for the independent variable ('I am worried about my health' 1)Totally disagree 2) Disagree 3)slightly disagree 4)nor agree nor disagree, 5)slightly agree, 6) agree, 7) totally agree). The other question is dichotomous - Do you consume yogurt? 1)Yes 2)No.

I would like to test this hypothesis using the variables above even though one is in Likert scale and the other is dichotomous.

Answer 1

Your hypotheses are not exactly appropriate for your polytomous independent variable.
I recommend rewording them as follows:

• H₀: Ratings of worry about health do not relate to yogurt consumption.
• H_A: Ratings of worry about health [do] relate to yogurt consumption.

This avoids dichotomizing people into groups who do / don't worry about health, which is unnecessary because you have richer information than that. In addition to who does and does not worry about health, you know who slightly worries, who totally does not worry, who's neutral, etc. Don't waste that!

To correlate your ordinal worry variable with the binary yogurt variable, I recommend calculating Kendall's $\tau$. This effect size estimate is appropriate for ordinal (including binary) data and facilitates nonparametric hypothesis testing. In r, the command is cor.test(x,y,method='kendall') where x and y are your two variables.

As an effect size estimate, I prefer to interpret $\tau$ on the scale of Pearson's r, as I am more familiar with that scale and expect most audiences to be as well. To convert $\tau$ to the scale of r, use $r = \sin\big(\tau\cdot\frac \pi 2 \big)$ as I mentioned in another answer. Full disclosure: I also borrowed much of the content of this answer from another I wrote earlier today.