Question

A non-profit organization is collecting data about how alcohol consumption affects academic performance. They want to perform a hypothesis test to see whether there is a relationship between how much alcohol a student consumes, and whether they are in good academic standing (GPA greater than or equal to 2.0). The results are summarized in the table below:

	Drinks 3+ drinks per week	Drinks 1-3 drinks per week	Does not drink	Total
Good academic standing	133	286	292	711
Poor academic standing	31	41	36	108
Total	164	327	328	819

a. Find the expected frequency for the number of students that drink 3+ drinks per week and are in poor academic standing, under the assumption of independence. Round your answer to 2 decimal places.

b. State the null and alternative hypothesis for the Chi-Squared test for independence: Select your answer from one of the following options.

• a.?0:There is a relationship between alcohol consumption and academic standing.??:Academic standing and alcohol consumption are independent characteristics.
• b.?0:It is impossible to be in good academic standing if you drink 3 or more drinks per week.??:It is possible to drink 3 or more drinks per week and be in good academic standing.
• c.?0:Drinking 3 or more drinks per week will increase the chance you are in poor academic standing.??:Drinking 3 or more drinks per week will increase the chance you are in good academic standing.
• d.?0:Academic standing is independent of how much a student drinks.??:There is a relationship between academic standing and how much a student drinks.

c. Using the Google Sheets command =CHITEST, find the p-value for the Chi-Squared test for independence. Round your answer to 4 decimal places.

d. Interpret your result:Select your answer from one of the following options.

• a.Fail to reject the null hypothesis. At a significance level of 0.05, there is not enough evidence to conclude there is a relationship between alcohol consumption and academic standing.
• b.Reject the null hypothesis. At a significance level of 0.05, there is enough evidence to conclude there is a relationship between alcohol consumption and academic standing.
• c.Fail to reject the null hypothesis. At a significance level of 0.05, there is enough evidence to conclude there is no relationship between alcohol consumption and academic standing.
• d.Reject the null hypothesis. At a significance level of 0.05, there is enough evidence to conclude that there is no relationship between alcohol consumption and academic standing.

Answer 1

a. Find the expected frequency for the number of students that drink 3+ drinks per week and are in poor academic standing, under the assumption of independence. Round your answer to 2 decimal places.

Answer : Expected frequency = ( row total * clumn total ) / n = ( 108*164) / 819 = 21.63

b. State the null and alternative hypothesis for the Chi-Squared test for independence: Select your answer from one of the following options.

Answer : The correct option is :-

• d.?0:Academic standing is independent of how much a student drinks.??:There is a relationship between academic standing and how much a student drinks.

c. Using the Google Sheets command =CHITEST, find the p-value for the Chi-Squared test for independence. Round your answer to 4 decimal places.

Answer :- The p-value is :- 0.8662

d. Interpret your result:Select your answer from one of the following options.

Answer :- Since , p-value > 0.05, the appropriate answer is ,

• a.Fail to reject the null hypothesis. At a significance level of 0.05, there is not enough evidence to conclude there is a relationship between alcohol consumption and academic standing.