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Math Problem - Speech or Presentation Example

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A manager of a Brisbane Motor Bike dealership reviewed a sample of 100 recent used Bike sales at the dealership. The sample mean price was $A19,300 and the sample…
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Math Problem
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Business Analysis Report Question: According to the Australian Motor Bike Dealers Association, the mean price for used premium Motor Bike is $A 20,000. A manager of a Brisbane Motor Bike dealership reviewed a sample of 100 recent used Bike sales at the dealership. The sample mean price was $A19,300 and the sample standard deviation was $A4,500. Letting m denote the population mean price for used Motor Bikes at the dealership, test
Null and alternative hypothesis:
Ho: null hypothesis
Ha. Alternative hypothesis
Ho: m = $A 20,000
Ha: m < $A 20,000
Level of significance:
a= 0.05
a) Critical value and rejection rule:
The value of z-score corresponds to the significance level of the null hypothesis is known as critical value. In left tailed test, the area under below this critical value is known as critical area or rejection area for null hypothesis. According to the rejection rule, if the value of Z calculated by the test statistic lies in critical area, then we reject the null hypothesis in favour of alternative hypothesis. On the other hand, if the value of test statistic does not fall in critical area then null hypothesis is accepted and alternative hypothesis is rejected.
The given test is a left tailed test. The significance value given in the question is 0.05, so the z-score corresponds to 0.05 is -1.645. The critical area for the given testing is the area less than -1.645 or the area left to the -1.645.
b) Test statistic:
Z = (M – U)/ S
M= sample mean price for used premium Motor Bike is $A20,000
U= population mean price for used premium Motor Bike is $A20,000
S = standard deviation / root of size of sample
M =19,300
U=20,000
S = 4,500/10 = 450
Put all the values in test statistic, we get
Z = (19,300 - 20,000)/ 450
Z = -1.56
Conclusion and Recommendation
In the particular z-test, the value of test statistic -1.56 is greater than -1.645, that is why it does not lie in rejection region, so null hypothesis is accepted and alternative hypothesis is rejected. The above test shows that the population mean price for used Motor Bikes at the dealership is $A 20,000.
The statistical assessment shows that the sample of 100 used cars has actually helped the manager of the company to determine the actual mean price of used cars in the market. This statistical data analysis can be used in future to determine the potential prices of the cars. In future the manager can use historical pricing data to price the products and it will be recognised as historical based pricing methodology. For example, in future if the manager of Brisbane Motor Bike wants to determine the potential price of its specific model motor bike, he can collect the sample of same model motor bikes from the market and he can determine the potential price for the bike. The price data can be collected from the market. In this way, the manager will not only be able to price his products rightly but he will be also able to keep his prices market competitive, thereby, attracting customers. Read More
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