
“[S]uppose we hypothesize that the true B_{1} takes a particular numerical value, e.g., B_{1} = 1. Our task now is to “test” this hypothesis.”
“In the language of hypothesis testing a hypothesis such as B_{1} = 1 is called the null hypothesis and is generally denoted by the symbol H_{0}. Thus H_{0}: B_{1} = 1. The null hypothesis is usually tested against an alternative hypothesis, denoted by the symbol H_{1}. The alternative hypothesis can take one of three forms:
H_{1}: B_{1} > 1, which is called a onesided alternative hypothesis, or
H_{1}: B_{1} < 1, also a onesided alternative hypothesis, or
H_{1}: B_{1} not equal 1, which is called a twosided alternative hypothesis. That is the true value is either greater or less than 1.”
The first thing we need to do to test our hypothesis is to calculate at tTest statistic. The theory behind the statistic is beyond the scope of this article. Essentially what we are doing is calculating a statistic which can be tested against a t distribution to determine how probable it is that the true value of the coefficient is equal to some hypothesized value. When our hypothesis is B_{1} = 1 we denote our tStatistic as t_{1}(B_{1}=1) and it can be calculated by the formula:
t_{1}(B_{1}=1) = (b_{1}  B_{1} / se_{1})
Let’s try this for our intercept data. Recall we had the following data:
Intercept

b_{1} = 0.47
se_{1} = 0.23
t_{1}(B_{1}=1) = (0.47 – 1) / 0.23 = 2.0435
So t_{1}(B_{1}=1) is 2.0435. We can also calculate our ttest for the hypothesis that the slope variable is equal to 0.4:
X Variable

b_{2} = 0.31
se_{2} = 0.03
t_{2}(B_{2}= 0.4) = ((0.31) – (0.4)) / 0.23 = 3.0000
So t_{2}(B_{2}= 0.4) is 3.0000. Next we have to convert these into pvalues. The pvalue "may be defined as the lowest significance level at which a null hypothesis can be rejected...As a rule, the smaller the p value, the stronger is the evidence against the null hypothesis." (Gujarati, 113) As a standard rule of thumb, if the pvalue is lower than 0.05, we reject the null hypothesis and accept the alternative hypothesis. This means that if the pvalue associated with the test t_{1}(B_{1}=1) is less than 0.05 we reject the hypothesis that B_{1}=1 and accept the hypothesis that B_{1} not equal to 1. If the associated pvalue is equal to or greater than 0.05, we do just the opposite, that is we accept the null hypothesis that B_{1}=1.
Calculating the pvalue
Unfortunately, you cannot calculate the pvalue. To obtain a pvalue, you generally have to look it up in a chart. Most standard statistics and econometrics books contain a pvalue chart in the back of the book. Fortunately with the advent of the internet, there’s a much simpler way of obtaining pvalues. The site Graphpad Quickcalcs: One sample t test allows you to quickly and easily obtain pvalues. Using this site, here’s how you obtain a pvalue for each test.Steps Needed to Estimate a pvalue for B_{1}=1
 Click on the radio box containing “Enter mean, SEM and N.” Mean is the parameter value we estimated, SEM is the standard error, and N is the number of observations.
 Enter 0.47 in the box labelled “Mean:”.
 Enter 0.23 in the box labelled “SEM:”
 Enter 219 in the box labelled “N:”, as this is the number of observations we had.
 Under " 3. Specify the hypothetical mean value" click on the radio button beside the blank box. In that box enter 1, as that is our hypothesis.
 Click “Calculate Now”

P value and statistical significance:
The twotailed P value equals 0.0221
By conventional criteria, this difference is considered to be statistically significant.
Be Sure to Continue to Page 3 of "Hypothesis Testing Using OneSample tTests".