Hypothesis Tests

When stating the conclusion to your hypothesis test, use the following structure.
If the pvalue is less than the significance level:
"I calculated a pvalue of #. This pvalue is less than our assumed (or stated  if given) significance level of 0.05. Therefore, we reject the null hypothesis. The data supports the claim that ... whatever alternative hypothesis is .... "
OR
If the pvalue is greater than the significance level:
"I calculated a pvalue of #. This pvalue is more than our assumed (or stated  if given) significance level of 0.05. Therefore, we fail to reject the null hypothesis. The data fails to support the claim that ... whatever alternative hypothesis is
Note: Never use the words prove or true anywhere in your conclusion.
If the pvalue is less than the significance level:
"I calculated a pvalue of #. This pvalue is less than our assumed (or stated  if given) significance level of 0.05. Therefore, we reject the null hypothesis. The data supports the claim that ... whatever alternative hypothesis is .... "
OR
If the pvalue is greater than the significance level:
"I calculated a pvalue of #. This pvalue is more than our assumed (or stated  if given) significance level of 0.05. Therefore, we fail to reject the null hypothesis. The data fails to support the claim that ... whatever alternative hypothesis is
Note: Never use the words prove or true anywhere in your conclusion.
Example
A political pollster claims that Mitt Romney will win over 50% of the votes in the state of New Hampshire during the Republican primary.
Provided significance level = .05
Hypothesis:
(p represent the proportion of Republican voters in the state of New Hampshire who will vote for Mitt Romney)
Ho: p = 0.5
Ha: p > 0.5
Correct conclusion if the calculated pvalue is less than the significance level:
"I calculated a pvalue of 0.02. This pvalue is less than the stated significance level of 0.05. Therefore, we reject the null hypothesis. The data supports the claim that Mitt Romney has the support of over 50% of the Republic voters in the state of New Hampshire"
Correct conclusion if the calculated pvalue is greater than the significance level:
"I calculated a pvalue of 0.08. This pvalue is greater than the stated significance level of 0.05. Therefore, we fail to reject the null hypothesis. The data fails to support the claim that Mitt Romney has the support of over 50% of the Republic voters in the state of New Hampshire"
A political pollster claims that Mitt Romney will win over 50% of the votes in the state of New Hampshire during the Republican primary.
Provided significance level = .05
Hypothesis:
(p represent the proportion of Republican voters in the state of New Hampshire who will vote for Mitt Romney)
Ho: p = 0.5
Ha: p > 0.5
Correct conclusion if the calculated pvalue is less than the significance level:
"I calculated a pvalue of 0.02. This pvalue is less than the stated significance level of 0.05. Therefore, we reject the null hypothesis. The data supports the claim that Mitt Romney has the support of over 50% of the Republic voters in the state of New Hampshire"
Correct conclusion if the calculated pvalue is greater than the significance level:
"I calculated a pvalue of 0.08. This pvalue is greater than the stated significance level of 0.05. Therefore, we fail to reject the null hypothesis. The data fails to support the claim that Mitt Romney has the support of over 50% of the Republic voters in the state of New Hampshire"