Part 1

Joe V. Lentement opens his mail one day to find his College Entrance Examination Board scores. On looking, he finds his score reported to be 345 (this test is assumed normally distributed with a mean of 570 and a standard deviation of 85). He calls his friend Ace Student to tell him of the news and asks him, `Did I do OK?` Ace replies politely, `Well, to be honest, not terrific. But you did better than some.`

1. What percent of students taking this test scored the same or lower than Joe?

Joe asked Ace, `What did you get?` Ace replied, `I forget the exact score, but I was in the top 0.5% of the test taking group.`

1. What did Ace score on the CEEB.

Joe calls another classmate, Mary N. Crowd, and asks how she scored. `Well, like, me and my friends, we all scored between 460 and 480 you know? And, like, we`re really happy to have done so well, you know?`

1. What percent of the test takers scored within this range?

Part 2

Later that night, Joe`s significant other comes home and finds him sitting dejectedly in front of the TV. He tells her about his performance and she says, `Joe, no one test proves anything. Tell you what. I`ll get us supper tonight. Why don`t you go outside and enjoy the warm weather.`

Joe sits in his favorite spot. `Gosh, it`s getting warmer every day. And I swear those crickets are even louder tonight.` Joe takes out his notebook and records the day`s temperature, as he has done every day for the past several years. He also counts how fast the crickets are chirruping, something he began taking interest in just last year. The information is recorded below (and is available in Excel format as well as Stata format):

 Day of Week Temperature Number of Chirrups/minute Tuesday 81 47 Wednesday 84 50 Thursday 89 58 Friday 93 65 Saturday 84 51 Sunday 81 45 Monday 75 42
1. Report the mean, median, variance and standard deviation for the week`s temperatures and the number of chirrups.

Joe thinks out loud, `I think these bugs change their chirrups as the temperature changes.`

1. How are temperature and chirrups related? (What is their covariance? What is their correlation? What do these numbers mean?)
2. Joe speaks to another friend about this. This friend is an entomologist and says, `Joe, there is a relationship! Increased temperature causes crickets to chirp faster! Everyone knows this.`
1. Run a regression with number of chirps as a function of temperature.
2. Report on the values and meaning of the intercept and the slope--what do these numbers mean and how are they used?