Question

Suppose that a sales tax on soda will be added in a random sample of communities to measure the impact on soda consumption. We wish to determine whether average per capital consumption of taxed soda is less than 50 gallons a year. Write the hypothesis using words.

Answer 1

Based on the given information, the hypothesis would be.

The average per capita consumption of taxed soda is less than 50 gallons a year.

In symbols, the hypothesis is

`\begin{gathered} H_o\colon\mu=50 \\ H_a\colon\mu<50 \end{gathered}`

Since the inequality sign is "less than".

It's important to know that the hypothesis is the thing we want to prove, in this case, we want to prove an average number with a specific parameter.

Also, notice that the system of hypothesis includes a null hypothesis and an alternative hypothesis.

The null hypothesis is the main hypothesis we have to prove because all statistical analysis requires it. Also, the null hypothesis is the opposite of the alternative hypothesis that's why we used "more than or equal to" 50.