Final answer:
To test the hypothesis that 70% of millennials pray at least once a week against a sample finding of 296 out of 467, a hypothesis test using the sample proportion, hypothesized proportion, standard error, z-score, and p-value from the standard normal distribution table is performed. The null hypothesis is rejected if the p-value is less than 0.05.
Step-by-step explanation:
To test the claim that 70% of millennials pray at least once a week, we need to perform a hypothesis test. Given the sample size of 467 millennials, with 296 found praying at least once a week, we can set up the null hypothesis (H0) as the proportion of millennials who pray at least once a week being 70% (p = 0.70) and the alternative hypothesis (H1) as the proportion being different from 70%.
First, calculate the sample proportion by dividing the number of millennials who pray by the sample size (296/467). Next, we find the standard error using the formula for the standard error of a proportion, which is √[p(1-p)/n], where p is the hypothesized proportion under the null hypothesis, and n is the sample size. Afterward, calculate the z-score by using the formula (sample proportion - hypothesized proportion) / standard error. Finally, refer to the standard normal (z) distribution table to find out the p-value. If the p-value is less than the chosen alpha level (usually 0.05), we reject the null hypothesis; otherwise, we do not reject it.