Numerade

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Ivan Kochetkov

Numerade educator

(c) Carry out your test to determine if the two variables are correlated. 3. A new drug is being developed to lower cholesterol in patients with high levels of cholesterol. A trial has been set up to test its efficacy with 10 subjects. For each subject, their cholesterol level will be measured; they then take the drug for one year, after which their cholesterol level is measured again. These levels before and after the programme are denoted as Xi and Yi respectively. Let Di be the difference Di = Yi - Xi. The following information is available from the trial: ?Di = -31.71 and ?Di² = 120.358. Answer the following four question parts. (a) Write down a suitable investigative hypothesis for this research. From this, set out the Null and Alternate Hypothesis and the other elements of a suitable statistical test for this investigation. (b) Carry out this test using the data given. (c) Redo the test if the manufacturer of the drug now claims it will lead to a reduction of at least 2 units. (d) State the best method to explain what the data is showing about the effect of the drug.

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ANSWERED

Eduard Sanchez

Numerade educator

Answer four of the following six questions. Each question carries 10 marks. 1. Solve the differential equation given here with boundary conditions using an integrating factor and identify what type of curve the solution is. dy/dx = -y/x The boundary condition is y = 2 when x = 1. 2. Solve the equation in the previous question using a different method of solution.

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ANSWERED

Ivan Kochetkov

Numerade educator

2. The vaccination rates against Covid-19 and the current ICU hospitalisation rates from Covid-19 over the last few weeks have been gathered for 13 regions of similar population size and density in the European Union. An investigation is to be done to see if the vaccination rates are affecting the ICU hospitalisation rates. (a) State the Null and Alternative Hypotheses for an appropriate test to determine if the two variables are correlated. (b) The correlation coefficient calculated from the data was r = 0.919. Explain how already having the value of r from the previous question part will affect the structure of your test. (c) Carry out your test to determine if the two variables are correlated.

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ANSWERED

Ivan Kochetkov

Numerade educator

Answer four of the following five questions. Each question carries 10 marks. Explain the terms 'Selection bias' and 'Confirmation bias', giving examples. Set out how the formal scientific method would be applied to an investigation into Ohm's law, Hooke's law or the increase in global mean temperatures.

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Tim Thornhill

Numerade educator

4. A company operates a tollgate on an isolated road. It has been established that for the month of October, cars arrive at this booth at a rate of one every 2 minutes. (a) Calculate the probability that a car arrives within the next 4 minutes from a given starting time. (b) Calculate the probability that 3 cars arrive in a ten-minute period for the toll booth.

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ANSWERED

Ivan Kochetkov

Numerade educator

Answer four of the following five questions. Each question carries 10 marks. 1. Give a definition of an event, an experiment and the probability of an event. The second part of your answer should include a reference to frequencies. Give an example of an event for which it is difficult to define a probability, explaining why.

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Donna Densmore

Numerade educator

Question 1.c: Use the Chain Rule to differentiate the following function ( y ) with respect to ( x ) : ( y=(4 x-2)^{2} ). Multiply your answer out fully.

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Claire Rochford

Numerade educator

a(-3, 1) and b(2, -2) are two points on a straight line. (i) Find the equation of the line ab. ["the line ab" means the straight line that contains the points a and b] (ii) What is the slope of the line ab? (iii) The point c lies on the line ab. The r coordinate of the point c is -8. What is the y coordinate of the point c? (iv) Calculate the distance between the points a and b, correct to 2 decimal places.

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Robin Corrigan

Numerade educator

3.c) In answering parts (i), (ii), and (iii) below, make it absolutely clear how you arrived at your answers. (i) How many numbers greater than 3,000 but less than 10,000 can be made using only the digits 1, 2, 3, 5, 7, 9 - with no repetitions of those digits? (ii) How many of those numbers are even? (Ii) Hence, use the subtraction method to calculate how many of these numbers are odd.

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Jonathon Brumley

Numerade educator

Question 2 – Statistics 2.a) The grouped frequency distribution table below shows the ages of a sample of 25 people. Plot the data on a histogram. | Age Category | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | | :--- | :--- | :--- | :--- | :--- | :--- | | Frequency | 2 | 5 | 8 | 6 | 4 | 2.b) Use the data in the table above to calculate the following: (i) using mid-interval values, calculate the mean age of the people, correct to the nearest whole number, (ii) using the mid-interval values, write down the ages of the 25 people above as a list of 25 numbers. Hence, calculate the median age of the people, correct to the nearest whole number. 2.c) Based on the mean and median values you calculated in part 2b), is the data in the frequency distribution above skewed to the left, skewed to the right, or not skewed? Explain your answer.

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TARA b.