Question

Please provide details how to solve it with excel.thank you!

1) Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 153 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 68 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 85 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use αα = 0.01.

	Pain Free: Yes	Pain Free: No	Total
Treatment	13	55	68
Control	4	81	85
Total	17	136	153

a) What is the correct null hypothesis?

• H0H0: Migraine pain relief is independent on receiving acupuncture.
• H0H0: Migraine pain relief is dependent on receiving acupuncture.
• H0H0: p1=p2=p3=p4p1=p2=p3=p4
• H0H0: p1≠p2≠p3≠p4p1≠p2≠p3≠p4

b) Fill in the expected values, round answers to at least 2 decimal places.

Expected Values	Pain Free: Yes	Pain Free: No
Treatment
Control

Answers show on last attempt	Pain Free: Yes	Pain Free: No
Treatment
Control

c) Find the test statistic, round answer to at least 3 decimal places.

d) What is the p-value? Round answer to at least 3 decimal places

e) What is the correct conclusion?

• There is no statistical evidence that migraine pain relief is dependent on receiving acupuncture.
• There is statistical evidence that migraine pain relief is dependent on receiving acupuncture

2)

The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. A researcher wants to determine whether health and happiness level are related. Test the researcher's claim at the αα = 0.05 level of significance.   

		Health
		Excellent	Good	Fair	Poor
Happiness	Very Happy	271	261	82	20
	Pretty Happy	247	567	231	53
	Not Too Happy	33	103	92	36

*Source: General Social Survey

1. Determine the null and alternative hypotheses.
   • H0:H0:Health and happiness are independent.
     Ha:Ha: Health and happiness are dependent.
   • H0:H0: Health and happiness have the same distribution.
     Ha:Ha: Health and happiness follow a different distribution.
   Correct
   
2. Determine the χ2 test statistic. Round to two decimal places.
   χ2 =
   
3. Determine the pp-value. Round to four decimal places.
   p-value =
   
4. Make a decision.
   • Fail to reject the null hypothesis.
   • Reject the null hypothesis.
   
   
5. Make a conclusion.
   • There is sufficient evidence to support the claim that health and happiness are related.
   • There is not sufficient evidence to support the claim that health and happiness are related.

Answer 1