Question

Regular ATM Non regular ATM
n = 200 n = 200
x-bar = 143 x-bar = 133
The managers of a regional bank in Florida believe that customers who regularly use their ATM cards (regular is defined as at least one time per week) are more profitable to the bank overall than customers who do not regularly use their ATM cards. A sample of 200 of the bank’s customers in each category was selected. An accounting was performed to determine the profit generated from each customer. The following sample data were observed. Regular ATM Non regular ATM n = 200 n = 200 x-bar = 143 x-bar = 133 Assume the following population standard deviations: 30 and 34, for regular ATM and non-regular ATM, respectively.
Using a level of significance of 0.05, what conclusion should the bank’s manager reach based on the sample data? Show all the five steps of the hypothesis testing.

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 ]