A researcher examined the admissions to a mental health clin

A researcher examined the admissions to a mental health clinic’s emergency room on days when the moon was full. For the twelve days with full moons from August 1971 through July 1972, the numbers of people admitted were:

5 13 14 12 6 9 13 16 25 12 14 20

Calculate the two-sided P-value test for the null hypothesis that these data are a random sample from a normal distribution with a population mean equal to 11.2, the average number of admissions on other days.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   11.2  
Ha:    u   =/   11.2  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    +/-   2.20098516      
              
Getting the test statistic, as              
              
X = sample mean =    13.25          
uo = hypothesized mean =    11.2          
n = sample size =    12          
s = standard deviation =    5.512382755          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.288264735          
              
Also, the p value is              
              
p =    0.2240923          
              
Comparing t and tcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Thus, there is no significant evidence that the mean number of people admitted on full moons is different from 11.2 a day. [CONCLUSION]