# Z score and T test

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?

need to show breakdown of answer(s).

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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.