Question

A random sample of 774 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 equals 0.05. Num Categories 7 Test​ statistic, chi-squared 2990.817 Degrees of freedom 6 Critical chi-squared 12.592 Expected Freq 110.5714 ​P-Value 0.0000 Determine the null and alternative hypotheses. Upper H 0​: ▼ At least two days of the week have a different frequency of being selected. All days of the week have an equal chance of being selected. At least one day of the week has a different chance of being selected. All days of the week have a different chance of being selected. Upper H 1​: ▼ All days of the week have an equal chance of being selected. All days of the week have a different chance of being selected. At least one day of the week has a different chance of being selected. At least two days of the week have a different frequency of being selected.

Answer 1

Answer: A random sample of 774 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.

Solution:

Determine the null and alternative hypothesis.

Null hypothesis Ho: All days of the week have an equal chance of being selected

Alternative hypothesis Ha: All days of the week have a different chance of being selected.

Test statistic χ2 = 2990.817

df = 6

Critical value of χ2 = 12.592

P-value = 0.0000

Since, P-value (0.0000) < α (0.05) significance level.

Reject the null hypothesis Ho.

There is sufficient evidence to support the claim that all days of the week have a different chance of being selected.

Or

Reject the null hypothesis Ho.

There is insufficient evidence to support the claim that all days of the week have an equal chance of being selected.