A Bank wishes to determine the mean income of its credit car

Osvaldo Apodaca 2021-12-16 Answered
A Bank wishes to determine the mean income of its credit card holders and more specifically wants to investigate whether there are any differences in the mean income between males and females. Confidence interval as a statistical inference method has been considered to respond this objective.
You are required to
1) Comment on the choice of confidence intervals as a statistical inference method for the above. Describe how you will proceed to determine the corresponding confidence intervals.
2) Explain how you would use confidence intervals as evidence suggesting that in average males and females income differ.
Use Numerical examples to illustrate as and when required.
(Word count around 250 words)
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Expert Answer

Tiefdruckot
Answered 2021-12-17 Author has 46 answers
Step 1
Since, we have to investigate whether there are any differences in the mean income between males and females we perform the t-test for two groups where the test statistics is given by,
t=(x1x2)(μ1μ2)(n11)s12+(n21)s22n1+n22(1n1+1n2)
Where:
n1, n2= sample size for the male female groups
s1, s2= sample standard deviations for the two groups
x1, x2= sample means for the male and female groups.
Step 2
To compute confidence intervals we can choose the confidence levels to be 0.01, 0.05, 0.10, and 0.20.
Thus, we can compute 99%, 95%, 90%, 80% confidence intervals.
Using the above t-test statistic we can compute the confidence interval as below:
CI=(x1x2)±tα2, (n1+n22)(n11)s12+(n21)s22n1+n22(1n1+1n2)
Step 3
Based on the confidence interval the following conclusions can be made:
If the calculated confidence interval does not contain zero in it, then we can conclude that the average males and females’ income differ.
If the calculated confidence interval contains zero in it, then we can conclude that the average males and females’ income do not differ.

We have step-by-step solutions for your answer!

Matthew Rodriguez
Answered 2021-12-18 Author has 32 answers
Step 1
Suppose, random variables X and Y denote income of male and female credit card holders respectively.
Here, two different groups (male and female) are used to collect data. Further we do not know population standard deviation (or variance). So, we have to use test statistic corresponding to two sample t-test.
Corresponding test statistic is given by
t=(xy)(μxμy)s×1nx+1ny
Here,
First sample size nx
Second sample size ny
Sample mean of first sample x
Sample mean of second sample y
Pooled sample standard deviation is given by
s=(nx1)×sx2+(ny1)×sy2nx+ny2
Degrees of freedom v=nx+ny2
For 100(1α)% confidence interval we have,
P(tα2, v<t<tα2, v)=1α Using R-code 11α2,v
P(tα2, v<(xy)(μxμy)s×1nx+1ny<tα2, v)=1α
P(stα2, v1nx+1ny<(xy)(μxμy)<stα2, v1nx+1ny)=1α

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