Answered: A random sample of 200 Gold accounts at…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A random sample of 200 Gold accounts at Top Bank showed that 28 were overdrawn. When 300 Silver accounts at the same bank were randomly checked, it was found that 36 were overdrawn. Can the bank manager conclude that there is an equal proportion of Gold and Silver account holders who were overdrawn? Test this hypothesis at a 5% level of significance.

Let Gold account =n1 and Silver account = n2

Critical value at 10% level of significance:1.645

Critical value at 5% level of significance:1.96

Critical value at 1% level of significance:2.576

Calculate the test stat and conclusion
State the decision rule
State the null hypothesis
State the alternative hypothesis

Expert Solution

Step 1

For 200 Gold accounts :

sample size = $N_1= 200$

Sample proportion = $\hat p_1 = \frac{X_1}{N_1} = \frac{ 28}{ 200} = 0.14$

sample size = $N_2 = 300$

sample proportion = $\hat p_2 = \frac{X_2}{N_2} = \frac{ 36}{ 300} = 0.12$

Pooled proportion = $\bar p = \displaystyle \frac{ X_1+X_2}{N_1+N_2}= \displaystyle \frac{ 28 + 36}{ 200+300} = 0.128$

Null and Alternative Hypotheses :

$\begin{array}{ccl} H_{0} : p_{1} & = & p_{2} (T h e r e i s a n e q u a l p r o p o r t i o n o f G o l d a n d S i l v e r a c c o u n t h o l d e r s w h o w e r e o v e r d r a w n) \\ H_{a} : p_{1} & \neq & p_{2} \end{array}$