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# Z score and T test

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Z test
At a retail store, customer survey is South Dallas the average household income of 75 household showed \$90K with standard deviation of \$25K. At another store in North Dallas, the household income of 60 households surveyed showed \$120K with standard deviation of \$30K. At significance level of 0.07, can a research analyst conclude that population means are different?

T test
A random sample of 20 car loans in Ben's finance shows household income of \$95K with standard deviation of \$18K. A random sample at Citi-Finance of 15 car loans showed household income of \$105K with standard deviation of \$16K. At significance level of .10, is there a difference in the population means? What inferences could you draw from this test?

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#### Solution Preview

Please see the attachments for explanations.

Answer
H0: There is no significant difference in the average house hold income in the two cities.
H1: There is significant difference in the average house hold income in the two cities.
The test statistic used is
Significance level  =0.07
Decision rule: Reject the null hypothesis if the calculated value of Z is greater than the critical value of Z.
Details
Z Test for Differences in Two Means

Data
Hypothesized Difference 0
Level of Significance 0.07
Population 1 Sample : South Dallas
Sample Size 75
Sample Mean 90
Population Standard Deviation 25
Population 2 Sample : North Dallas
Sample ...

#### Solution Summary

The solution provides step by step method for the calculation of Z score and probability. Formula for the calculation and Interpretations of the results are also included.

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