Final answer:
Testing a hypothesis using the p-value approach involves comparing the calculated p-value with the significance level to determine whether to reject or not reject the null hypothesis. A small p-value indicates that the observed result is unlikely if the null hypothesis were true, which typically leads to rejection of the null hypothesis.
Step-by-step explanation:
To test the hypothesis using the p-value approach with H0: p=0.7 versus p>0.7, we first need to calculate the p-value from the test statistic based on the sample data. The null hypothesis H0 posits that the population proportion p is equal to 0.7, whereas the alternative hypothesis Ha suggests that the population proportion p is greater than 0.7.
If the p-value is less than the significance level (α), we reject the null hypothesis. Conversely, if the p-value is greater than α, we fail to reject the null hypothesis. For instance, if the computed p-value from the sample data is 0.04 and our α is set at 0.05, we would reject the null hypothesis because the p-value is less than α, indicating that there is sufficient evidence at the 5% significance level to conclude that the true population proportion is greater than 0.7.
It is also important to note the interpretation of the p-value. If the null hypothesis is true, then the probability of observing a sample proportion as extreme or more extreme than the one observed is equal to the p-value. Therefore, a small p-value suggests that the observed result is unlikely under the assumption that the null hypothesis is true, leading to the rejection of the null hypothesis.