1. An experiment was done to determine if a pair of dice is “fair”, that is, the probability that each number on each die is the same. Tom tosses the dice 50 times and determines that the mean sum of the sample is 6.6, with a standard deviation of 1. 133. According to the mechanics of tossing two dice, the mean should be 7. Determine if this is a fair dice at the .05 level of significance. Also determine the p-value.

1. Determine if a t or a z hypothesis test should be used.
2. Is this a one-tail or a two-tail hypothesis test?
3. Find H0 and H1.
4. Use both the Classical Approach and the P-Value Approach to determine whether to reject or fail to reject the null hypothesis.
5. Interpret the conclusion.

. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model. ∑X = 50 ∑X2 = 200 ∑Y = 75 ∑Y2 = 1600 ∑XY = 400 Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

a. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.
∑X = 50
∑X² = 200
∑Y = 75
∑Y² = 1600
∑XY = 400

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

b. 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 $3600 and perform significance test for the slope.

Fremont High School has 2100 students. One of the statistics teachers at the school is interested in whether an intervention program based on self-management improves attendance. They randomly choose 80 students and randomly assign half of them to either an experimental condition (self- management class) or a control condition (distractor class on popular culture). At the end of the semester, they measure the number of days missed for each student. The teacher expects that the students in the self-management class will be absent for fewer days than the control group.

1) What is the population in this experiment?

2) What is the sample in this experiment?

3) What is the response variable in this experiment?

4) If the teacher calculates the average number of absences for the group of 80 students, then that average would be a______. A. Parameter B. Statistic

5) If the teacher calculates the average number of absences from all the 2100 students, then that average would be a_______. A. Parameter B. Statistic

6) The teacher records the number of absences for each student. This record is her______.

Number of absences is a______.

A. data; continuous B. data; discrete

7) Number of absences is a______.

A. Ratio B. Interval C. Nominal D. Ordinal

Problem 3.22. The response time in milliseconds was determined for three different types of circuits that could be used in an automatic valve shutoff mechanism. The results from a completely randomized experiment are shown in the following table:

Circuit Type...........Response Time

a) Test the hypothesis that the three circuit types have the same response time. Use α=0.01.

b) Use Tukey’s test to compare pairs of treatment means. Use α = 0.01.

c) Use the graphical procedure in Section 3.5.3 to compare the treatment means. What conclusions can you draw? How do they compare with the conclusions from part (b)?

d) Construct a set of orthogonal contrasts, assuming that at the outset of the experiment you suspected the response time of circuit type 2 to be different from the other two.

e) If you were the design engineer and you wished to minimize the response time, which circuit type would you select?

f) Analyze the residuals from this experiment. Are the basic analysis of variance assumptions satisfied?

PLEASE MAKE SURE IS A "MINITAB" ANSWER, OTHERWISE... DON'T BOTHER. THANK YOU.

A company that stamps gaskets out of cork sheets and wants to compare the mean number of gaskets produced per hour for three different types of stamping machines. The company wants to use the data to determine whether one machine is more productive than the other. To answer these questions, the manufacturer decides to conduct an experiment with each of the machines operating for six 1-hour time periods assigned in a random order to eliminate the possibility of bias. The data for the experiment, the number of gaskets (in thousands) produced per hour is shown below. (a) State the hypotheses and conduct an analysis of variance at α = 0.05 to test the hypotheses. Create a boxplots of the data as part of the oneway ANOVA. (b) Plot and analyze the residuals from the experiment and comment on model adequacy. (c) Is there sufficient evidence to indicate that any machine is more productive than the others? Machine 1 Machine 2 Machine 3 431 427 440 436 442 448 401 394 389 404 441 418 421 409 418 425 393 422

5a. When 4.355 grams of a hydrocarbon, C_xH_y, were burned in a combustion analysis apparatus, 14.72 grams of CO₂ and 3.014 grams of H₂O were produced.

In a separate experiment, the molar mass of the compound was found to be 26.04 g/mol. Determine the empirical formula and the molecular formula of the hydrocarbon.

• Enter the elements in the order presented in the question.
  

  empirical formula =

  molecular formula =

5b.
A 12.57 gram sample of an organic compound containing C, H and O is analyzed by combustion analysis and 17.83 grams of CO₂ and 10.95 grams of H₂O are produced.

In a separate experiment, the molar mass is found to be 62.07 g/mol. Determine the empirical formula and the molecular formula of the organic compound.

• Enter the elements in the order C, H, O
  

  empirical formula =

  molecular formula =

5c.

A 4.550 gram sample of an organic compound containing C, H and O is analyzed by combustion analysis and 6.452 grams of CO₂ and 3.963 grams of H₂O are produced.

In a separate experiment, the molar mass is found to be 62.07 g/mol. Determine the empirical formula and the molecular formula of the organic compound.

• Enter the elements in the order C, H, O
  

  empirical formula =

  molecular formula =

Craig is setting up a fluidized bed in which a reaction will take place. The reactants are combined with compressed air to act as the fluid in the bed and the particles inside of the bed are catalysts for the reaction. Craig sets up an experiment to determine which particle size is most effective for his reactor. In experiment 1, Craig utilizes particles that are 1 mm in diameter. In experiment 2, Craig uses particles that are 5 mm in diameter. Craig finds that his reaction reaches completion much faster when the 5 mm diameter particles are used so he decides to go forward with utilizing the larger particles for his reactor. What is one (1) potential drawback of utilizing the larger particles over the smaller ones? (answer must relate to the operation of the fluidized bed)

You can assume that the total mass of the particle bed will be equivalent no matter the size of the particles, the particles have the same density and that the particles are priced the same per gram over all size ranges. The tube in which the fluidization takes place is the same for both particle types. Additionally, the bed must become fluidized to achieve best reaction results.