I've received a few emails about the take home test already (which is awesome), and a couple things were brought to my attention. Check out the hints/help below:
#10 and #11:
These questions are both binomial probability models. We know they are binomial because we are given a sample size for each. To answer these questions we need to use the formulas for the mean and standard deviation for a binomial probability. The mean of a binomial probability model is = np. In other words, mean = mu = np. The standard deviation of the binomial probability model is found by sqrt(npq). That is, standard deviation = sigma = squareroot(npq). You can also find these formulas in chapter 17.
#12:
There are two ways to do this question. One approach is to use the binomial probability on our calculator (you decide if it's pdf or cdf). If you use this method your answer will not match the multiple choice options (but it is correct); choose the option closest to your answer.
Another approach is to use the Normal model to find a binomial probability. We did not learn this before break. Any time that np > 10 and nq > 10 we can use a Normal model (instead of binomcdf). To find the mean and standard deviation of the Normal model we would have to use the formulas described above (for #10 and #11). Then, we will have a new mean and standard deviation, and we can use these values to calculate a z-score and use normalcdf (like any other Normal model problem). If you use this method your answer will match the multiple choice options.
Both methods are correct.
Keep the questions coming! If I get more questions that I feel will be helpful for everyone, I'll keep posting my responses to emails on the blog!
Extra Credit Opportunity:
Want/need some extra credit?
You can earn 6 points on a quiz grade if you do the following:
- Listen to the "Stat Rap" under the "Statistics Music" link on the right.
- Write down at least 12 statistics references you hear in the song. You must write the exact lyrics of the song. Number these references.
- Then, below each reference, briefly explain what the reference means, statistically speaking. Do not simply define the terms, you must interpret the statistical meaning in the context of the song!
- Your explanations must be correct! You will earn 1/2 point for each correct lyric and explanation; if you want to be sure you'll earn all 6 points, feel free to provide extra references!
**This only applies to the "Stat Rap," not the "Stat Rap Remix." (We'll save that one for later...)
Example:
1. "I state the null hypothesis there ain't no way you're stopping this."
- The null hypothesis is the first thing you state in a hypothesis test, and this is the first line of a song.
2. "Crossin' all my T's like my name was Billy Gosset."
- William Gosset developed the t-distribution that is used in Statistics."
