Question

Regular ATM Non regular ATM

Answer 1

Answer:

Conclusion

     We can conclude that the believe of the  mangers of the regional banks is true

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  200

    The  mean for  Regular user is  $\= x_1 = 143$

    The mean for Non regular  is  $\r x_2 = 133$

   The standard deviation for  Regular is  $\sigma_1 = 30$

    The standard deviation for Non regular  is $\sigma _2 = 34$

   The level of significance is  $\alpha = 0.0 5$

The null hypothesis is

       $H_0 : \r x_1 = \r x_2$

The alternative hypothesis is  

      $Ha: \r x_1 > \r x_2$

The test statistics is mathematically represented as

        $Z = \frac{\r x _1 - \r x_2}{\sqrt{\frac{\sima_1^}{n} } + \frac{\sigma_2^2}{n} }$

substituting values

        $Z = \frac{143 - 133}{\sqrt{\frac{30^2}{200} } + \frac{34^2}{200} }$

      $Z = 3.12$

Now the critical value of the level of significance obtained from the z-table is

      $t_{\alpha } = 1.645$

 So given the fact as seen from the above calculation that  $Z > t_{\alpha }$

Then the Null hypothesis would be rejected as there is no sufficient evidence to back up the null hypothesis  [Which stated that the profit from both users are the same ]