Aj Davis Project Part B
INTRODUCTION
Base on the data collected in the previous samples, the manager has made an alternative hypothesis on the following:
A) The average (mean) annual income was less than $50,000
B) The true population proportion of customers who live in an urban area exceed 40%
C) The avarage (mean) number of years lived in the current home is less than 13 years D) The avarage (mean) credit balance for suburban costumers is more than $4,300
Using the sample data, we will perform hypothesis tests on the aforementioned situations above in order to determine if we can support the manager's belief in each case. The hypothesis tests will be computed with 95% confidence intervals to ensure accuracy in our alternative hypothesis opinion.
The avarage (mean) annual income was less than $50,000
The manager is correct. The avarage (mean) annual income is less than $50,000. After running the data located in Appendix A, notice that the avarage (mean) annual income came out to 43.74. This means that the avarage income is $43,740, which is less than $50,000.
Furthermore, after running a 95% confidence interval on this data, we can say that we are 95% confidence interval on this data and we are 95% certain that the avarage (mean) annual income falls at 47,210 on the higher end of the tail, which is less than 50,000. Since the p-value of .002 is less than the alpha value of .05, we can say beyond a reasonable doubt that the manager's alternative hypothesis is correct and we will reject the null hypothesis because we have sufficient evidence for rejection.
One-Sample T: Income ($1000)
Test of mu = 50 vs < 50
95% Upper
Variable N Mean StDev SE Mean Bound T P
Income ($1000) 50 43.74 14.64 2.07 47.21 -3.02 0.002
The true population proportion of customers who lives in an urban area exceed 40%
Base on the data collected in the previous samples, the manager has made an alternative hypothesis on the following:
A) The average (mean) annual income was less than $50,000
B) The true population proportion of customers who live in an urban area exceed 40%
C) The avarage (mean) number of years lived in the current home is less than 13 years D) The avarage (mean) credit balance for suburban costumers is more than $4,300
Using the sample data, we will perform hypothesis tests on the aforementioned situations above in order to determine if we can support the manager's belief in each case. The hypothesis tests will be computed with 95% confidence intervals to ensure accuracy in our alternative hypothesis opinion.
The avarage (mean) annual income was less than $50,000
The manager is correct. The avarage (mean) annual income is less than $50,000. After running the data located in Appendix A, notice that the avarage (mean) annual income came out to 43.74. This means that the avarage income is $43,740, which is less than $50,000.
Furthermore, after running a 95% confidence interval on this data, we can say that we are 95% confidence interval on this data and we are 95% certain that the avarage (mean) annual income falls at 47,210 on the higher end of the tail, which is less than 50,000. Since the p-value of .002 is less than the alpha value of .05, we can say beyond a reasonable doubt that the manager's alternative hypothesis is correct and we will reject the null hypothesis because we have sufficient evidence for rejection.
One-Sample T: Income ($1000)
Test of mu = 50 vs < 50
95% Upper
Variable N Mean StDev SE Mean Bound T P
Income ($1000) 50 43.74 14.64 2.07 47.21 -3.02 0.002
The true population proportion of customers who lives in an urban area exceed 40%