A cleaning company is interested in determining if good results in window cleaning are dependent on the brand of cleaning product, or some other variable such as cleaning technique. They asked their clients to complete a survey after each clean and results are recorded in the table below:
The company conducts a χ2 test of independence at a 5% significance level.
State the null hypotheses for the problem.
State the alternate hypotheses for the problem.
State the number of degrees of freedom.
Calculate the test statistic, χ2, correct to two decimal places.
Find the p-value, correct to two decimal places.
State, giving a reason, if the null hypothesis should be rejected.
The following table of data was collected from a survey where people were asked what their favourite movie genre was:
Researchers conduct a χ2 test of independence at a 1% significance level.
State the null hypotheses for the problem.
State the alternate hypotheses for the problem.
State the number of degrees of freedom.
Calculate the test statistic, χ2, correct to two decimal places.
Given that the critical value is 11.34, state whether the null hypothesis should be accepted.
At the last Commonwealth Games, 220 spectators were asked which of four events they preferred to watch. Results are displayed in the following table:
In order to see whether age had any influence over favorite sport, researchers conducted a χ2 test of independence at a 5% significance level.
State the null hypotheses for the problem.
State the alternate hypotheses for the problem.
State the number of degrees of freedom.
Calculate the test statistic, χ2, correct to two decimal places.
Find the p-value, correct to five decimal places.
State, giving a reason, if the null hypothesis should be rejected.
Explain what is meant by the 5% level of significance.
