In a Study, of treckments for Vony peinful "Chuster! with Oxyg em and 148 patents were govem aplacis Consistimg of Cndivamng air. Amng te 150 pabtents n the the crryqim treatment amup, 116 were free from headacle 5 minutn affen traatnent. Aming the 148 patremts given the placebo, 29 Were fre frm hendedhe • Is minutós after tractrent Cbaned on datqa from high florw Ozyqım for tratmint of Chuster Headache" by Cohens, Bums cnd Goadby, Jaunnad of flre Americam Malical ass.ciatuen, vo 308, No. g0) We Want to use Oi ol Sigifon claim that fle Ý Test the cluim Vsimg a hypotuusis fast bY Test fae chauirn by nstructmg y Basod un the resurts, a tue oeygen nce laves to test fraatmont s effoctrve triatment fectiyee
State the hypotheses.
Let p1 denotes the proportion of people free from head ache after 15 minutes in Oxygen treatment.
Let p2 denotes the proportion of people free from head ache after 15 minutes in Placebo treatment.
That is, there is no evidence to conclude that proportion of people free from head ache after 15 minutes in Oxygen treatment is effective compared to the Placebo treatment.
That is, there is evidence to conclude that proportion of people free from head ache after 15 minutes in Oxygen treatment is effective compared to the Placebo treatment
Decision rule:
Obtain the value of the test statistic.
The value of test statistic is obtained below:
The formula of proportion 1 is defined as,
The formula of proportion 2 is defined as,
The formula for test statistic is,
The value of sample proportion1,
The value of sample proportion2,
Thus, the value of test statistic is 9.84.
Obtain the P-value.
Use Excel to obtain the probability value for Z=9.84
Follow the instruction to obtain the P-value:
- Open EXCEL
- Go to Formula bar.
- In formula bar enter the function as“=NORMSDIST”
- Enter the test statistic Z as 9.84.
- Click enter
EXCEL output:
From the Excel output, the P-value is 1.0000
The P-value in the right tail is 0.0000 (=1–1)
Thus, the P-value is 0.0000.
The conclusion is obtained as shown below:
Use the level of significance is 0.01.
The p-value is less than level of significance.
By rejection rule, reject the null hypothesis.
That is, the Oxygen treatment is effective compared to the Placebo treatment.
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