Question

What’s your sign? The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS of $4344$ people:

If births are spread uniformly across the year, we expect all $12$ signs to be equally likely. Do these data provide convincing evidence at the $1\%$ significance level that all $12$ signs are not equally likely?

Short answer

There isn't enough information to back up the assertion that all $12$ signals aren't equally likely.

Step-by-step solution

Given information

Calculation

The null and alternative hypotheses:

$$\begin{gathered} H_0:p_1=p_2=...=p_{12}=\frac{1}{12}=0.0833 \\ {H}_a:Atleastoneofthe{p}_i’sisincorrect. \end{gathered}$$

Using excel:

Chi-square test statistic $=19.76$

The $p-$value $=0.0487$

Decision: The$p-value>0.01$fail to reject $H_0$

There isn't enough information to back up the assertion that all $12$ signals aren't equally likely.