Perpendicular to the line 2x + 3y = 12, passing through the point (7,3)

Question 1 (Essay Worth 10 points) (08.01 LC) Tina conducted a survey to find the favorite weekend activity of the people in her state. She asked 10 of her neighbors what their favorite weekend activity is. Tina concludes that boating is the favorite weekend activity of the people in her state because 70% of her neighbors like to go boating on weekends. Use at least two sentences to explain why Tina's sample may not be valid. Make sure to use facts to support your answer.

Tina's neighbors are a biased sample; maybe she's in a rich neighborhood or one by the water. Even if unbiased, a sample size of ten is will give a very variable estimate; a larger sample is needed for statistical significance.

Question 2 (Essay Worth 10 points) (08.01 MC)Below are the data collected from two random samples of 500 American adults on the number of hours they work per day (rounded to the nearest hour):

Number of hours of work per day 678910

Sample A: Number of adults 609014515055

Sample B: Number of adults 708014014565

Ryan concludes that adults spend a mean of 8 hours working each day. Malia thinks the mean is 9 hours. Who is correct—Ryan or Malia? Explain your answer in two or three sentences. Make sure to use facts to support your answer.

The mean is the weighted average; let's do the two samples separately:

A:

B:

Both groups average out to around 8.1 hours, so Ryan is more correct. Even without the detailed calculation, the 6 and 10 categories average out to 8 and the 7 and 9 categories average out to around 8.3 and at around 40% of the data move the average up from 8 to 8.1.

Question 3 (Essay Worth 10 points) (08.02 LC)The table below shows the size of nine families selected at random from two neighborhoods in a large city:

Family Size (in number of people)

Neighborhood Q254325365

Neighborhood S232372332

Which neighborhood appears to have a bigger family size? Explain your answer using two or three sentences. Make sure to use facts to support your answer.

Just adding differences, we get +2+2-5+3+3+3, about 8 more people in Q. So Q seems bigger. The respective averages are

The average size of the sampled households is almost one person larger in Q. The sample size of 9 households per neighborhood is pretty small; the result may not be significant. We could perform a t-test to test if Q was significantly bigger that S.

Question 4 (Essay Worth 10 points) (08.03 MC)The dot plots below show the ages of students belonging to two groups of music classes:

( graph is the picture below)

Based on visual inspection, which group most likely has a lower mean age of music students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.

Group A clearly is the younger students, with the data clustering around a mean of 10 compared to a mean of around 15 for group B. Group A doesn't have anybody older than 14 or so; around half of the Group B students are 15 and older.