Essay type

1. Test H₀: μ ≤ 8 versus H_A: μ > 8, at α = 0.05 and 0.01, given n = 25, X ¯ = 8.07 and s = 0.16. Assume the sample is selected from a normally distributed population.

2. Test H₀: Π = 0.2 versus H₁: Π ≠ 0.2 with p = 0.28 and n = 100 at alpha = 0.05.

3. Test at α =.05 and 0.10 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 265 favor the system?

4. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3800.

5. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.

∑X = 40
∑X² = 200
∑Y = 70
∑Y² = 545
∑XY = 300

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation and check the relation between coefficient of correlation and coefficient of determination. Finally, perform the test of significance of the slope coefficient.