Classical Hypothesis Testing in Statistics

STATISTICS

STATISTICS
Question a
The hypotheses for this classical hypothesis testing approach are as given below;
H0 (Null Hypothesis): The prices for SPDR Gold EFT and Spot Gold do not differ.
H1 (Alternative Hypothesis): The prices for SPDR Gold EFT and Spot Gold differ.
In the development of the hypotheses above, the interest for the study is considered. In
this case, the interest is primarily in observing the prices for SPDR Gold EFT and Spot Gold.
The purpose for this observation is determining whether the prices for SPDR Gold EFT and Spot
Gold are significantly different.
Thus, this information forms the basis for the development of the necessary research
hypotheses with the price being the variable of interest. The null hypothesis is based on there
being no difference between the prices for SPDR Gold EFT and Spot Gold hence; H0 (Null
Hypothesis): The prices for SPDR Gold EFT and Spot Gold do not differ. While the alternative
hypothesis is based on there being a difference between the prices for SPDR Gold EFT and Spot
Gold hence; H1 (Alternative Hypothesis): The prices for SPDR Gold EFT and Spot Gold differ.
Question b
Since interest in this study is to determine whether there is a difference in prices for
SPDR Gold EFT and Spot Gold, then a Two Sample T-test is the appropriate test for this study.
The Two Sample T-test is a statistical test that compares the means of two different populations
to determine whether the two populations significantly differ from each other (O'Neil & Schutt,
2013; Everitt & Skrondal, 2010).
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STATISTICS
In this study, the two populations are the SPDR Gold EFT and Spot Gold. The Two
Sample T-test therefore compares the mean prices in the samples drawn from these two
populations in order to establish whether the prices for SPDR Gold EFT and Spot Gold
significantly differ from each other.
Step 1
The mathematical representation of the hypotheses is therefore given as below:
H0 : x1=x2
H1 : x1 ≠ x2
Step 2
The level of significance for this study has been provided for as; α level of significance =
0.01. this value will be used for the testing of the hypothesis stated in step 1 above. This implies
that for this study, the probability of rejecting the null hypothesis when it is true is 0.01.
Step 3
The test statistics for the Two Sample T-test is as given below (Barbara & Susan, 2014);
t= [ x1 −x2 ] −d
SE
Where,
x1=mean of sample ¿ population 1
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