Statistics for Business: Comparing Google and Amazon Stock Performance

This assignment presents a comprehensive statistical analysis of Google and Amazon stock returns. It begins by defining the requisite hypotheses, including null and alternative hypotheses, and sets the level of significance. The solution employs t-tests to compare the average return of Google stock against a benchmark, and F-tests to compare the standard deviations of returns between Google and Amazon stocks. Furthermore, it calculates a 95% confidence interval for the difference in mean returns of the two stocks to determine if the returns differ significantly. The analysis includes p-value comparisons against the level of significance to either reject or accept the null hypotheses. The statistical tests and their corresponding results are presented with clear explanations and conclusions regarding the stock performance and associated risks. The assignment aims to provide a robust framework for statistical inference and decision-making in the context of financial data analysis.

STATISTICS FOR BUSINESS
STUDENT ID:
[Pick the date]

TASK 2
(ii) The requisite hypotheses are defined as follows.
Null Hypothesis (H0): μ = 5% i.e. average return on Google stock is not different from 5%.
Alternative Hypothesis (H1): μ ≠ 5% i.e. average return on Google stock is different from 5%.
Level of significance = 5%
The requisite test statistics to be used here would be t statistics. This is because the
population standard deviation (i.e. standard deviation of GOOGLE stock returns over the
entire listing period) is not given. Thus, one-sample t test would be used to compare the
population mean.
T-stat = (X-μ)/s/n0.5
Here X (sample average) = 1.238%
S (sample standard deviation) = 5.786%
n (sample size) = 60
T statistic = (1.238-5)/(5.786/600.5) = -5.04
Degree of freedom = 60-1 = 59
For df=59 and tstat =-5.04, p value = 0
Since p value < level of significance, hence the evidence presented is sufficient to warrant
null hypothesis rejection and alternative hypothesis acceptance. Hence, it may be concluded
that average return on Google stock is different from 5%.
(iii) The requisite hypotheses are defined as follows.
Null Hypothesis (H0): σgoogle2 = σamazon2 i.e. the standard deviation of returns of Google and
Amazon stock does not differ significantly.
Alternative Hypothesis (H0): σgoogle2 ≠ σamazon2 i.e. the standard deviation of returns of Google
and Amazon stock does differ significantly.

Level of significance = 5%
The appropriate test statistic in the given scenario would be F statistic. The appropriate
hypothesis test has been performed using Excel with the relevant output indicated as follows.
The two tail p value would be 0.0035*2 = 0.007
Since p value < level of significance, hence the evidence presented is sufficient to warrant
null hypothesis rejection and alternative hypothesis acceptance. Hence, it may be concluded
that the standard deviation of returns of Google and Amazon stock does differ significantly.
This would imply that the risks related to the two stocks are unequal.
(iv) The requisite hypotheses are defined as follows.
Null Hypothesis (H0): μGOOGLE - μAMAZON = 0 i.e. the average returns on the two stocks does
not differ significantly.
Alternative Hypothesis (H1): μGOOGLE - μAMAZON ≠ 0 i.e. the average returns on the two stocks
does differ significantly.
Level of significance = 5%
In order to determine if the null hypothesis can be rejected or not, 95% confidence interval
for the difference of the mean returns for the two stock population needs to be found which
has been found using Excel. The requisite output in this regards is shown as follows.

The requisite 95% confidence interval for the difference in returns of two stock population is
(-4.3158,0.8394). It is evident that the hypothesised value of 0 is also included in the
confidence interval determined above. As a result, the available evidence does not lead to
rejection of null hypothesis. Thus, the alternative hypothesis cannot be accepted. Hence, it
may be concluded that the average returns on the two stocks does not differ significantly and
hence can be assumed as same.