Final answer:
The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the p-value is 0.0294, which indicates that there is strong evidence against the null hypothesis. This means that the proportion of women over 40 who regularly have mammograms is significantly less than 78%.
Step-by-step explanation:
The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the null hypothesis is that the proportion of women over 40 who regularly have mammograms is less than 78%. The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
From the given information, the test statistic is z = -2.231. To find the p-value, we need to calculate the probability of getting a z-score less than or equal to -2.231 in a standard normal distribution. This can be done using a standard normal distribution table or a calculator.
The p-value is the area to the left of -2.231 under the standard normal curve. According to the table, the area to the left of -2.231 is approximately 0.0147. However, since the alternative hypothesis is p < 0.78, we need to find the area to the left of -2.231 and multiply it by 2 to get the two-sided p-value.
Therefore, the p-value accurate to 4 decimal places is 0.0294.