A new product claims to releive indigestion within 10 minute

A new product claims to releive indigestion within 10 minutes. Past studies have indicated that the population standard deviation is 2 minutes. And, when 35 individuals used the product, the mean time until releif was 9.25 minutes. Is the company\'s claim accurate at the 95% confidence level?

Give a statistically appropriate conclusion to the hypothesis test

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   10  
Ha:    u   <   10  
              
As we can see, this is a    1   tailed test.      
              
Thus, getting the critical z,              
              
zcrit =    -1.644853627          
              
Getting the test statistic, as              
              
X = sample mean =    9.25          
uo = hypothesized mean =    10          
n = sample size =    35          
s = standard deviation =    2          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.218529919          
              
Also, the p value is              
              
p =    0.013259361          
              
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the relief time is indeed less than 10 minutes. [CONCLUSION]