Statistics and Probability Answers

A real estate agent has compiled some data on the selling prices of recently sold homes (in $10 000) compared to their distance from the nearest school (in km).

Distance From School (km) 8 7 9 10 4 11 2 11 1 2 12 5 9 8 3 1 6

Selling Price ($ 10 000) 20 17 9 25 10 5 6 31 31 29 2 18 23 12 24 2 15

The real estate agent runs a linear correlation and concludes that, with a correlation coefficient of 𝒓 ≐ −𝟎. 𝟏𝟎, there is no relationship between the distance from a school, and the selling price. Is this completely true? Comment on the validity of his result and provide an explanation for the result. (Hint: Look at a scatter plot of the data. It is not necessary to draw the scatter plot on your paper.)

Which of the following statements is true?

A) Extrapolation is always reliable when using a non-linear regression model.

B) The coefficient of determination must be 1 for a regression model to be useful.

C) Data can sometimes be accurately represented by several regression models.

D) A polynomial regression for 𝒏 data points requires a polynomial function of degree 𝒏 to fit the data perfectly.

The Graduate Record Exam (GRE) is a standardized test required to be admitted to many

graduate schools. A high score in the GRE makes admission more likely. According to the

Educational Testing Service, the mean score for takers of GRE who do not have training

courses is 555 with a standard deviation of 139. Brainpower Philippines (BP) offers expensive

GRE training courses, claiming their graduates score better than those who have not taken any

training courses. To test the company’s claim, you as a statistician randomly selected 30

graduates of BP and asked their GRE scores. The random sample of 30 graduates he obtains

recorded a mean score of 560 in GRE. (Level of Significance α = 0.05)

Identify the test statistic to be used and the following;

1. x̅= ___

2. s or σ = ___

3. H0: ___

4. H1: ___

5. μ = ___

6. α = ___

7. ZC or tC = ___

8. Zα or tα = ___

9. Decision rule: ___

10. Draw the rejection region: ____

11. Decision: ___

12. Conclusion:

A researcher is testing the hypothesis that all teenagers spend an average of 8 hours on their computers during the weekends. He knows that the standard deviation is 0.3 hour. He selects a sample of 144 teenagers and decides to reject the null hypothesis when the sample mean is 8.5 hours or less.

A. What us the probability of that the researcher commits a type I error?

B. If the true population mean is 7 hours, what is the probability that the he commits a type II error?

C. Determine the power of test.

Women weight are on average 65kg with a standard deviation of 5kg.Mens weight are on average 75kg with a standard deviation of 10kg.Estimate the percentage of the population whose weight are more than 55kg assuming the number of men and women are equal.