Question

would the answer for A be:

H0: u1-u2>= 0

Ha: u1-u2<0

if not why not?? and whats the answer if incorrect??

2. The managers of a regional bank in Florida bel once a week) are more profitable to the bank overall than those who do not regularly Swal bank in Florida believe that customers who regularly use their ATM cards (at least Sample of 200 of the bank's customers in each category was selected. An accounting was k overall than those who do not regularly use their ATM cards. A in each category was selected. An accounting was performed to determine the 2004 profit generated from each customer, and the following sample data were oosc TOTAL 22 PTS 122 Regular ATM users Non-regular ATM users n = 200 n = 200 * = $145 X2 = $135 S = $30 S = $35 a) Based on the sample information, what conclusion should the bank managers reach? (Use a = 0.05) Hypothyeses (2 pts) H: H.: Test Statistic: 2 pts) ii. iii. Decision Rule (critical value approach): (2 pts)

Answer 1

Let , $\mu_1$ be the population mean of the regular ATM users and $\mu_2$ be the population mean of the non-regular ATM users.

i) Hypothesis : $H_0:\mu_1=\mu_2$ Vs $H_a:\mu_1>\mu_2$

ii) The test statistic is ,

$Z=\frac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\to N(0,1)$

$=\frac{145-135}{\sqrt{\frac{30^2}{200}+\frac{35^2}{200}}}=3.07$

Critical value : $Z_{\alpha}=Z_{0.05}=1.64$

Rejection rule : If $Z_{STAT}>Z_{\alpha}=1.64$ , then reject the null hypothesis , accept otherwise

Decision : Here , $Z_{STAT}=3.07>Z_{\alpha}=1.64$

Therefore , reject the null hypothesis

Conclusion : Hence , The managers of a regional bank in Florida believe that customers who regularly use their ATM cards are more profitable to the bank overall than those who do not regularly use their ATM cards.