Question

a random sample of 772 subjects was asked to identify the day of the week that is best for quality family time. consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. the table below shows goodness - of - fit test results from the claim and data from the study. test that claim using either the critical value method or the p - value method with an assumed significance level of $\alpha = 0.05$.

determine the null and alternative hypotheses.

$h_0$: all days of the week have an equal chance of being selected.

$h_1$: at least one day of the week has a different chance of being selected.

identify the test statistic.

$\chi^2=\square$ (type an integer or a decimal.)

Explanation:

Step1: Identify the test statistic from the table

The table provides the test statistic for the chi-square goodness - of - fit test. We can directly obtain the value of the test statistic \(\chi^{2}\) from the given table.
From the table, the value of the test statistic \(\chi^{2}\) is given as 10.462.

Answer:

\(10.462\)