two parts: Part I – Qualitative; Part II – Quantitative.

Analysis

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Question one

Discussion on whether the trading volume of the stock is normally distributed

The following are the results after running the data in SPSS on trading volume.

Data skewness is 3.742; its kurtosis is 21.678. An acceptable range for skewness and kurtosis are (-1,1) and (-2,2), respectively, for any normally distributed data (Polat, 2017). The above two values for skewness and kurtosis are not within the range, indicating that the data is not normally distributed.

From the above, both tests of Kolmogorov and Shapiro show that the test p-value is less than 0.05 alpha level. If the significance is less than the alpha level, it means that the data is not normally distributed.

The histogram also confirms the above; it doesn't show normality. The Q-Q plot chart above also gives a visual representation of the volume in trading. If the data distribution follows a normal distribution, it means that the dots would mostly follow the trend line above (SPSS, 2020). As from the above, the data fails to cluster along the line that is further showing proof that the data is not normal.

Part three

Histogram of the mean value

Histogram of the standard deviation

Part Four

The mean and standard deviation of the sample data created are 55503343.90 and 1803179.793, and that for the volume standard deviation data are 23571236.94 and 3296183.246, respectively. The skewness and kurtosis for Volume mean are 0.635 and 0.253, respectively. The two do not lie between the range discussed of the data following a normal distribution. Thus, the volume formed from the sample mean does not show any sign of normality. The value for the volume standard deviation does not follow a normal distribution too.

The test for normality for the newly formed sample data is as shown above. The significance level for both Kolmogorov-Smirnov and Shapiro-Wilk is 0.000 and 0.001, respectively. Since both are less than 0.05 alpha level, it means that the calculated data is not normal.

The Q-Q graph above displays how the data points fails to align with the trend line indicating that they are not normal data points or the data fails to show normality.

The tests of normality above indicate that the level of significance is 0.000 for the two indicated tests. Since the two values are below 0.0 alpha level, it means that the data does not follow a normal distribution.

As can be viewed from the Normal Q-Q graph above, the standard deviation values do not follow the trend line, indicating that they are not following the normal distribution (Laerd, 2020).

Part Five

With a 95 percent confidence level, it means that the corresponding value from the z-statistics is 1.96. We are told that the average daily trade volume is 49829719, and the standard deviation is 21,059,637 shares. The formula gives sampling error

Z* sigma/ sqrt (n)

So, the minimum required sample size would be as shown below.

10,000,000 = 21,059,637/ sqrt(n)

Sqrt (n) = 21,059,637/10,000,000

Sqrt (n) = 2.1059637

n =2.10937 * 2.10937

n = 4.4308

An n of 4.4 would represent an approximate of around five members as the sample.

For a sampling error of 20,000,000, the sample size would be as follows?

20,000,000 = 21,059,637/ sqrt(n)

Sqrt (n) = 21,059,637/ 20,000,000

Sqrt (n) = 21,059,637

Sqrt (n) = 1.05 * 1.05

n= 1.108

n would be around 2 samples.

If N = 2013, then the calculations would be as follows

Sampling error would be calculated as 21,059,637/ sqrt (2013)

The sampling error would be given as 469385

Part Six

The independent t-test is calculated using the formula

Since M2017 = 46108055, S2017 = 34099055, n2017 = 251, M2018 = 87241844, S2018 = 50977722, n2018 = 238.

t= (46108055 – 87241844)/ sqrt (340990552/251 + 509777222/238)

t=-21986

The t-statistic is -21986, the df from the calculation is n for 2017 + n for 2018 – 2.

The calculation for df would be 251 +238 -2 which gives 487. From these values, the average trading volume in 2017 and 2018 is not statistically significant.

References Laerd. (2020). Testing for normality using SPSS Statistics. Retrieved from https://statistics.laerd.com/spss-tutorials/testing-for-normality-using-spss-statistics.php#:~:text=value%20of%20the%20Shapiro-Wilk,enhanced%20testing%20for%20normality%20guide. Polat. (2017). What is the acceptable range of skewness and kurtosis for normal distribution of data if sig value is <0.05? Retrieved from https://www.researchgate.net/post/What_is_the_acceptable_range_of_skewness_and_kurtosis_for_normal_distribution_of_data_if_sig_value_is_005#:~:text=Some%20says%20for%20skewness%20(−1,skewness%20is%20an%20acceptable%20range. SPSS. (2020). Test for Normality in SPSS. Retrieved from https://ezspss.com/test-for-normality-in-spss/