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Significance Pattern and Hypothesis Testing

1. The share of the national car manufacturers market in South Africa is shown in the table below:


VW 37
Toyota 30
Delta 15
BMW 10
Mercedes 8

A random sample of 2000 car owners in Pretoria revealed the following ownership pattern:

VW = 758 Toyota = 680 Delta = 300 BMW = 162 Mercedes = 100

Does the ownership pattern differ significantly from the National pattern?
Investigate at the 5% level of significance.

2. It is believed that call center operators should spend no longer than 10 minutes on each call, however a survey involving a random sample of 49 operators found a mean call duration of 11 minutes with a standard deviation of 3 minutes. Test the Hypothesis at the 1% level of significance.

Solution Summary

This solution provides the null and alternative hypothesis and conducts a chi-squared test and z-test to determine the test static which will be compared to the p-value. A decision is made to accept or reject the null hypothesis.