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 \\).
\\( 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}=10.462 \\) (type an integer or a decimal.)
identify the critical value.
\\( \chi^{2}=12.592 \\) (type an integer or a decimal.)
state the conclusion.
\\( h_{0} \\). there sufficient evidence to warrant rejection of the claim that the days of the week are selected with a uniform distribution. it that all days have the same chance of being selected.

Explanation:

Step1: Compare test statistic and critical value

The test statistic $\chi^2$ is 10.462, and the critical value $\chi^2$ is 12.592. Since $10.462 < 12.592$, we do not reject the null hypothesis $H_0$.

Step2: Determine evidence

When the test statistic is less than the critical value, we fail to reject $H_0$. This means there is not sufficient evidence to warrant rejection of the claim that all days have the same chance of being selected.

Answer:

First dropdown: Fail to reject
Second dropdown: is not
Third dropdown: appears