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y= α+ β x -- population regression function
α and β are population parameters.
Usually, these are not known and must be estimated from a sample of data drawn from that population.
y=a+bx -- sample regression function
a and b are sample estimates of the α and β.
A sample is a subset of a population. Usually it is impossible to test an entire population so tests are done on a sample of that population. These samples can be selected so that they are representative of the population in which cases the sample will have weights, strata, and clusters. But usually people use random samples. So it's not that the line is different, it's that the line comes from different data. In stats we have formulas that allow a sample to represent a population, if you have the entire population (again unlikely), you wouldn't need to use this sample formulas, only the population formulas.
2) A large p-value implies - D
A) rejection of the null hypothesis.
B) a large t-statistic.
C) a large act.
D) that the observed value act is consistent with the null hypothesis.
Correct answer(s): D
3) Regression model ones.
The following regression model is produced based on the relationship between the fuel economy (mpg) and horse power for 15 models of cars: MPG^ = 46.87 – 0.084HP
a. If the car you are thinking of buying has a 200 – horsepower engine, what does this model suggest your gas mileage would be?
b. The regression model MPG^ = 46.87 – 0.084HP relates car’s horsepower to their fuel economy (in mpg). Explain what the slope means.
ANSWER HERE!!! (2)
4) A random sample of records of sales of homes gives the Price (in 1000 US Dollars) and Size (in square feet) of 117 homes. The regression analysis of these home sales gives the model Price^ = 47.82 + 0.061Size
a. Explain what the slope of the line says about housing prices and house size.
b. What price would you predict for a 3000 – square – foot house in this market?
ANSWER HERE!!! (15)
5) A sample of 27 blue M&M chocolates with a mean weight of 0.8560 g. Assume that σ is known to be 0.0565 g. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean weight of all M&M chocolates is equal to 0.8535 g.
a. What is the test statistics? test statistic = 0.1839 Answer: 0.1839
b. What is the P-value? p-value = 0.8541
c. What is the conclusion about the null hypothesis (reject, fail to reject)?
d. What is the final conclusion in simple nontechnical terms?
6) A sample of 106 body temperatures with a mean of 98.200 F. Assume that σ is known to be 0.620 F. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean body temperature of the population is less than 98.60 F.
a. What is the test statistics?
b. What is the P-value?
c. What is the conclusion about the null hypothesis (reject, fail to reject)?
d. What is the final conclusion in simple nontechnical terms?
ANSWER HERE!!! (5 slides)
http://math.fau.edu/qian/course/sta2023/Note/L19-HT-mean.pdf