predict(m,new_data,se.fit=TRUE, level=0.95,interval="confidence") 截屏2024-05-05 22.49.36.png This indicates that the average mathematics test score, with a 95% confidence interval, is between 57.327 and 80.759 across all schools in the state where 50% of the instructors have at least one mathematics university degree, their mean age is 43 years, and their mean yearly income is $78,500.predict(m,new_data,se.fit=TRUE, level=0.95,interval="confidence") 截屏2024-05-05 22.49.36.png This indicates that the average mathematics test score, with a 95% confidence interval, is between 57.327 and 80.759 across all schools in the state where 50% of the instructors have at least one mathematics university degree, their mean age is 43 years, and their mean yearly income is $78,500.

Refer to the previous exercise and perform the following tasks.a) Predict for the Director of the Department of Education in Queensland the mean mathematics test score at a school in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500. What is the corresponding approximate 95% prediction interval? Calculate the point prediction first manually and then with R, and the approximate 95% prediction interval manually only.b) Predict for the Director of the Department of Education in Queensland the mean mathematics test score at all schools in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500.c) Predict with 95% confidence the mean mathematics test score at a school in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500. How does this prediction interval compare to the approximate 95% prediction interval you obtained in part (a)? d) Estimate with 95% confidence the mean mathematics test score at schools in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500. How does this confidence interval compare to the prediction interval you obtained in part (c)?

A survey of 8 university student revealed a mean income of $180.98 with a standard deviation of $143.042. Calculate a 95% confidence interval for the mean income of all students:

Predict for the Director of the Department of Education in Queensland the mean mathematics test score at all schools in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500.

52. Analyzing College Grade Point Average. Recall that in exercise 49 , the admissions officer for Clearwater College developed the following estimated regression equation relating final college GPA to the student's SAT mathematics score and high-school GPA. \[ \hat{y}=-1.41+0.0235 x_{1}+0.00486 x_{2} \] where \[ \begin{aligned} x_{1} & =\text { high-school GPA } \\ x_{2} & =\text { SAT mathematics score } \\ y & =\text { final college GPA } \end{aligned} \] A portion of the associated computer output follows. LO 4, 5, 6

Question 2381 random elementary schools were asked for their average exam scores (sample mean = 535, sample standard deviation = 7). Calculate the 98% confidence interval.1 point(528.00, 542.00)(533.15, 536.85)Not possible to calculate based on this information.(533.41, 536.59)