Consider a coin toss experiment and the following assets. A gives £200 if the first is heads, £50 for tails. B gives £200 if the second is heads and £50 for tails. C is half of A plus half of B. A and B are independent. Show that the expected value of each asset isthe same. Show that C reduces risk and explain why this is so. [Hint: You need to calculate E(A), E(B), and E(C). Also calculate the standard deviation (or risk) of returns from each asset]

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 282 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status   Diseased   Not Diseased   Total
Vaccinated 54 124 178
Not Vaccinated 71 33 104
Total 125 157 282

Step 1 of 8:

State the null and alternative hypothesis.

Step 2 of 8:

Find the expected value for the number of subjects who are vaccinated and are diseased. Round your answer to one decimal place.

Step 3 of 8:

Find the expected value for the number of subjects who are vaccinated and are not diseased. Round your answer to one decimal place.

Step 4 of 8:

Find the value of the test statistic. Round your answer to three decimal places.

Step 5 of 8:

Find the degrees of freedom associated with the test statistic for this problem.

Step 6 of 8:

Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places.

Step 7 of 8:

Make the decision to reject or fail to reject the null hypothesis at the 0.025 level of significance.

Step 8 of 8:

State the conclusion of the hypothesis test at the 0.025 level of significance.

I did an experiment in which a cart on wheels is getting pulled by a pulley hanging off the surface. The pulley has a 50g hanger which causes the motion. The cart is 300g and then in different trials added one 50g weight, two, three, and then four. The slope was 0 degrees. My question is: Describe (and show with pictures) what forces change for each of the different configurations used.

. In an online experiment, participants were asked to react to a stimulus. Upon seeing a blue screen, participants were instructed to press a key and the reaction time was measured in seconds. The same participant is also asked to press a key when seeing a red screen, with the reaction time measured. (The first color tested was randomly selected for each participant.) The results of 6 randomly sampled participants are below. Is the reaction time to the blue stimulus different from the reaction time to the red stimulus at the 1% level of significance? (assume the population differences are approximately normally distributed)

participant 1 2 3 4 5 6

blue 0.582 0.481 0.841 0.267 0.685 0.450

red 0.408 0.407 0.542   0.402 0.456 0.533

Conduct a full hypothesis test. Be sure to:

• state the test and calculator test

• check conditions

1. state the hypotheses

2. find the differences between the pairs, sample mean, sample standard deviation, degrees of freedom and calculate the test statistic

3. state the level of significance

4. find the p-value and draw/shade the graph

5. make a decision

6. write a conclusion

3. An experiment consists of randomly rearranging the 10 letters of the word
QUARANTINE
into a sequence of 10 letters, where all possible orders of these 10 letters are equally likely. Find the probability of each of the following events:
(1) 2 the first three letters include no A’s;
(2) 3 the first three letters or the last three letters (or both) include no A’s;
(3) 2 the fourth letter is the first A;
(4) 3 the first letter and the last letter are the same;
(5) 2 the word ‘QUARANTINE’ is obtained;
(6)3 the sequence contains the word ‘RAN’

In a calorimetry experiment to determine the specific heat capacity of a metal block, the following data was recorded: Quantity Mass of the metal block 0.50 kg Mass of empty calorimeter + Stirrer 0.06 kg Mass of calorimeter + stirrer + water 0.20 kg Mass of water 0.14 kg Initial Temperature of metal block 55.5 ⁰C Initial Temperature of water and calorimeter 22 ⁰C Final Temperature of block- water system 27.4 ⁰C Take the specific heat capacity of water to be 4186 J/Kg °C. The calorimeter and stirrer are made of Copper. Specific heat capacity of Copper is 387 J/Kg °C. Ignore the mass of the stirrer. Use the data and the information given to: a) Calculate the specific heat capacity of the metal block. (Please show ALL work for full credit) b) From your result above, what is the metal block probably made up of? c) Calculate the final temperature of the block – water system if the mass of the water in the calorimeter is increased to 0.50 kg (the same as the mass of the metal block).

The following data was collected in a laboratory experiment conducted at 305.2 K.

A.) Determine the complete rate law for this simple chemical process A → B

B.) For the set of kinetic data in the problem above, if the rate doubles when the temperature increases to 415.4 K, what is the activation energy for the process?

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use a =.05.

An experiment is performed to study the fatigue performance of a high strength alloy. The number of cycles to crack initiation is measured for twenty specimens over a range of applied pseudo-stress amplitude (PSA) levels. Use the data in the table provided to fit the following three regression models with y = Cycles and x = PSA (note the natural log transform of y for all models):

PSA (x) Cycles (y)

80, 97379

80, 340084

80, 246163

80, 239348

100, 34346

100, 23834

100, 70423

100, 51851

120, 9139

120, 9487

120, 8094

120, 17956

140, 5640

140, 3338

140, 6170

140, 5608

160, 1723

160, 3525

160, 2655

160, 1732

iii. A simple linear regression model with a logarithm transformation on PSA: lny=δ0+δ1∙ln⁡(x) .

1) Using model (iii.), find a 95% confidence interval for the mean Cycles to crack initiation at a PSA of 130

1. A paper in the Journal of the Association of Asphalt Paving Technologies (1990) described an experiment to determine the effects of air voids on percentage retained strength of asphalt. For purposes of the experiment, air voids are controlled at three levels: low (2-4%), medium (4-6%), and high (6-8%). The data are shown in the following table:

1. Write down the Null and Alternative hypotheses to test if the different levels of air voids significantly affect mean retained strength. Define all the terms used.

2. Find the calculated Ftest statistic then answer what are the critical F value and the rejection region of H0 at α=5% ?

1. c. Test the hypotheses using the test statistic / critical value method (use your answers to (b), and (c)). Clearly interpret the test result in the context of the problem.

d. What is the P value for the test? Test the hypotheses using the P value. Do you get the same answer as (d)? If your answer is different, clearly interpret it.