An experiment was run to determine whether four specific firing temperatures affect the density of a certain type of brick. The following data was collected.

Set up a regression model to describe the experiment. State the model and all assumptions, interpret the meaning of each parameter. Show all the steps needed to estimate all model parameters, including writing down the X matrix and the Y vector. Can you estimate the value of β0?

In a famous experiment done at the end of the 19th century, two metal electrodes were placed in an evacuated glass tube. A high voltage was applied between them. By using an appropriate metal for the cathode (e.g., sodium or potassium), it was found that a current could be made to flow when the cathode was illuminated with blue light, but no current would flow when red light was used, no matter how bright the light. Einstein was able to explain this strange phenomenon, and as a result, this experiment was considered the first experimental demonstration of

A. the wave nature of light.

B. the particle nature of electrons.

C. the wave nature of electrons.

D. the particle nature of light.

1 (a-c)

You ask your graduate student to roll a die 5000 times and record the results.

a) Give the expected mean and standard deviation of the outcome.

b) The die roll experiment is repeated (though with a different graduate student – for some reason your previous student went to work with a different advisor). However in this case, the die is weighted so that a 6 shows up 11% of the time, a 1 shows up 25% of the time, and all remaining numbers show up 16% (each). Now what is the expected mean and sd of 5000 rolls?

c) What would happen if we changed the experiment to 10,000 rolls?

1. Does a person’s cholesterol level increase with age? Data collected from 1406 adults aged 45 to 62 (with a mean age of 54 years) produced the regression analysis shown. Assuming that the data satisfy the conditions for inference, examine the association between age and cholesterol level.

1. State the appropriate hypothesis for the slope.
2. Test your hypothesis and state your conclusion in the proper context using the t-statistic/p-value.
3. What’s the value of the standard error for the slope of the regression line? Explain what that means in this context.
4. Find a 90% confidence interval for the slope and interpret it in this context.
5. Find a 90% prediction interval for the cholesterol level of Santa Claus if he is 60 years old.
6. Find a 90% prediction interval for the mean cholesterol level of all adults aged 60.
7. The intercept is positive. Discuss its value and meaning.

Required information

[The following information applies to the questions displayed below.]
  
In 2018, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2020. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

5. Calculate the amount of revenue and gross profit (loss) to be recognized in each of the three years assuming the following costs incurred and costs to complete information. (Do not round intermediate calculations and round your final answers to the nearest whole dollar amount. Loss amounts should be indicated with a minus sign.)

The effects of three concentrations of the ripening hormone (ethylene) were tested on tomato yield and quality. Five tomato cultivars (Shady Lady, Merced, Santa, Chiquita, and Celebrity) were grown in 5 replications in the field. The hormone was applied 4 weeks after flowering. Fruits were harvested 4, 5 and 6 weeks after the hormone application. Number of fruits per plot was counted, and fruits of each plot were classified to three groups of red, yellow-red and yellow. Fruit yield (kg/plot) and sugar concentration were measured. Fruit texture and taste were surveyed in a population of 50 people. For the survey, a sample of the fruits from each plot was given to people to eat and score taste from 1 to 10, and fruit texture from 1-5.

Identify the:

Problem

1. Hypothesis:
   1. H₀:
2. 2. H₁:

Experimental unit:

Experimental material:

Control variable(s)

Independent variable(s):

Dependent variable(s):

7. 1. Quantitative variable(s):
   2. Qualitative variable(s):
8. 1. Continuous variable(s):
   2. Discrete variable(s):

Required information

[The following information applies to the questions displayed below.]

In 2021, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2023. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

4. Calculate the amount of revenue and gross profit (loss) to be recognized in each of the three years assuming the following costs incurred and costs to complete information. (Do not round intermediate calculations and round your final answers to the nearest whole dollar amount. Loss amounts should be indicated with a minus sign.)

Required information

[The following information applies to the questions displayed below.]

In 2021, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2023. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

5. Calculate the amount of revenue and gross profit (loss) to be recognized in each of the three years assuming the following costs incurred and costs to complete information. (Do not round intermediate calculations and round your final answers to the nearest whole dollar amount. Loss amounts should be indicated with a minus sign.)

Required information

[The following information applies to the questions displayed below.]

In 2018, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2020. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

rev: 09_15_2017_QC_CS-99734

4. Calculate the amount of revenue and gross profit (loss) to be recognized in each of the three years assuming the following costs incurred and costs to complete information. (Do not round intermediate calculations and round your final answers to the nearest whole dollar amount. Loss amounts should be indicated with a minus sign.)