Significance Pattern and Hypothesis Testing
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1. The share of the national car manufacturers market in South Africa is shown in the table below:
MANUFACTURER % OF SHARES
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.
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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.
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1. The share of the national car manufcturers market in South Africa is
shown in the table below:
MANUFACTURER % OF SHARES
VW 37
Toyota 30
Delta 15
BMW 10
Mercedes ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
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