And here are the homework answers so you can check yours--of course we want to make sure we're practicing correctly when we study!
**If you check over your answers and make any corrections/comments on your original response you can earn homework extra credit! Just show evidence (notes) that you checked over all of your reponses!**
Stamp: Linear Regression (Given Computer Output):
- Slope: According to the linear model, for each additional 1 hour a student spends studying, his/her predicted final exam score increases by approximately 2.697 points.
- Y-Intercept: According to the LSRL, if a students studies for 0 hours (if a student does not study), his/her predicted final exam score is roughly 62.328. (This is realistic).
- Coefficient of Determination = R^2: According to this model, about 56.7% of the variation in exam score can be explained by the changes in study hours. Other factors might include the student's course grade/performance and the difficulty of the exam.
- Residual = Actual - Predicted
- Actual score = 84
- Predicted score = 62.328 + 2.697(6) = 78.51
- Residual = 84 - 78.51 = 5.49.
- (This residual tells that we underestimated the final exam score for a student who studied for 6 hours by 5.49 points; remember, a positive residual is an underestimate).
Stamp: Probability (Spinner Question)
- a.) P(lands on # divisible by 3) = 3/10 = 0.3
- We have 3 numbers divisible by three on the spinner: 3, 6, and 9 out of 10 total sections.
- b.) P(all 6 spins land on a # divisible by 3) = (0.3) ^ 6 = 0.000729
- Remember, 7.29E-4 means you have to move the decimal 4 places to the left; this is the calculators form of scientific notation
- If you're stuck, write it out in words!
- "divisible by 3" and "divisible by 3" and "divisible by 3" and......
- c.) P(not all 6 spins are divisible by 3) = 1 - (0.3)^6 = 0.999271
- Focus on the question..."not all 6 spins are divisible by 3"
- Not = 1 -
- First, we'll find the probability "all spins are divisible by 3"
- Then, since we want "NOT all spins are divisible by 3" we'll subtract this answer from 1!
- On our probability test many students tried this: (0.7)^6; this is incorrect, because this represents the probability that all the spins are not divisible by 3, which is a different situation
- "not all divisible by 3" means they are not all divisible by 3; in other words, 0,1,2,3,4 or 5 spins can be divisible by 3, just not all of them
- "all not divisible by 3" means all of the spins are not divisible by 3; in other words, none are divisible by 3!
- d.) P(spin 50 times and at most 10 spins divisible by 3) = bincomcdf(50, 0.3, 10) = 0.0789
- Remember binomcdf is used for "cumulative" probabilities, or numbers of outcomes "below" or "to the left" of what we enter for our x value (10 in this case)
- Binompdf would give us the probability that exactly 10 spins land on a number divisible by 3....
- e.) P(first spin divisible by 3 is 4th spin) = (0.7)^3 * (0.3) = 0.1029
- OR, geometpdf(0.3, 4) = 0.1029
- If you're stuck here, just go back to your words!
- "not divisible by 3" and "not divisible by 3" and "not divisible by 3" and "divisible by 3"
Sampling Context: The Gallup Poll and TV...
- Population = all American citizens
- Population Parameter of Interest = % of all American citizens who identify each type of content that bothers them the most (% of all American citizens who are bothered by violence, by language, or by sexual situations)
- Sampling Frame: all American citizens with a phone
- Sample: the 1,475 Americans who were randomly called and surveyed
- Sampling Method: randomly generated phone numbers (this is a simple random sample, which is essentially "pulling names out of a hat"
- Yes, we can generalize our results to the population of "all American citizens" because the sample was collected randomly (simple random sample) and therefore should be representative of the population.
This is also a great time to start studying for your midterm!
- Use your Barron's book! Look over different topics we've learned and try a practice exam!
- Look over your take home test (passed back today) and figure out anything that was incorrect!
- Use your notes to review!
- Look at the outline of topics under the classroom powerpoints and assignments link on the right!
Tuesday in class we'll get back to our sampling methods! See you there!
Then, on Wednesday we'll have some classwork to do (I will be absent unfortunately) that will be graded. Finally, on Thursday and Friday we'll talk more about sampling and bias before the midterm! See you there!
Have an awesome 3 day weekend!
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