A national college researcher reported that 67%of students who graduated from high school in 2012 enrolled in college. Twenty-ni
1 answer:
Answer:
Mean is 19.43
Standard deviation is 2.5322
Step-by-step explanation:
For each student who graduated from high school in 2012, there are only two possible outcomes. Either they have enrolled in college, or they have not. The probability of a student having enrolled in college is independent of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
67% of students who graduated from high school in 2012 enrolled in college.
This means that
Sample of 29 high school graduates
This means that
Mean
Standard deviation
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Answer:
Step-by-step explanation:
Assuming conditions are met, the formula for a confidence interval (CI) for the difference between two population proportions is where
and
are the sample proportion and sample size of the first sample, and
and
are the sample proportion and sample size of the second sample.
We see that and
. We also know that a 98% confidence level corresponds to a critical value of
, so we can plug these values into the formula to get our desired confidence interval:
Hence, we are 98% confident that the true difference in the proportion of people that live in a city who identify as a democrat and the proportion of people that live in a rural area who identify as a democrat is contained within the interval {-0.2941,-0.0337}
The 98% confidence interval also suggests that it may be more likely that identified democrats in a rural area have a greater proportion than identified democrats in a city since the differences in the interval are less than 0.