The stakeholders of the stock markets in Bangladesh are trying their best to make better infrastructure of stock markets in comparison to other stock-markets in Asian nations. To bring the stock market in an operational and informational order, two stock markets have been set up in Bangladesh of which the Dhaka Stock Exchange (DSE) is one of them. Consequently, the traders of the markets are rolling fund, stakeholders and other philanthropist organizations are using data for estimating indices such as price per share, price earning ratio, current market price of the share etc. mainly to know whether the markets are running efficiently. The data on these indicators of 1st quarter of the financial years 2004, 2005, 2006 & 2007 have been collected to test the EMH (Efficient Market Hypothesis) because this hypothesis states that market prices instantaneously or fully reflect all relevant available information. It means that the market prices of the securities will always equal their intrinsic values. Thus, the hypothesis holds that the share price movements are random and systematic. According to this hypothesis, it is possible to earn normal returns by randomly choosing securities at a given risk level. This research attempts to test whether the series on the industry such as bank, insurance, service, food and allied and textile really follow the behavior of normal distribution. The different descriptive statistics, non-parametric estimators and ARCH models are used for testing the hypotheses. The results may be important to the planners, security analysts, investors and security exchange regulatory bodies for improving the market status in this connection. The estimated results are found very useful.