In the previous year the proportion of deposits in checking

In the previous year the proportion of deposits in checking accounts at a certain bank that were made electronically was 45%. The bank wishes to determine if the proportion is higher this year. It examined 20,000 deposit records and found that 9,217 were electronic. Determine, at the 1% level of significance, whether the data provide sufficient evidence to conclude that more than 45% of all deposits to checking accounts are now being made electronically.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.45
Ha:   p   >   0.45
As we see, the hypothesized po =   0.45      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.46085      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.003517812      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.084303697      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.001020146      
significance level =    0.01      

Comparing p < 0.01, we   REJECT THE NULL HYPOTHESIS.

Thus, there is significant evidence that more than 45% of all deposits to checking accounts are now being made electronically. [CONCLUSION]