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A University student is studying inflation and money supply. The following statistics were
provided to the student.
Money supply in rands R Inflation 28000 3,42 28000 3,60 21000 4,84 14000 7,81 35000 1,14 14000 8,51 14000 7,87 28000 2,89 21000 4,91 35000 1,89 35000 1,72 21000 4,47
i. Determine the dependent and independent variables and explain your selection.
[3]
ii. Find the straight-line regression equation that represent the relationship between
the dependent and independent variable. [7]
iii. What is the estimated inflation rate associated with a money supply of R31500?
[3]
iv. What is the money supply level associated with zero inflation rate [3]
v. Calculate and interpret the covariance between money supply and inflation rate.
[4]
vi. Calculate the correlation coefficient between the two-variable displayed in the
table? [3]
vii. What does the correlation coefficient tell us about the relationship of the two
variables in the table above? [2]
Your given ∑ 𝑥 = 44 , ∑ 𝑥2 = 174, ∑ 𝑥𝑦 = 1324, in addition you also given the values of y
as:
Y 26 28 24 18 35 24 36 25 31 37 30 32
3a. calculate the Pearson correlation coefficient [7]
3b. estimate the y value associated with x=4 [8].
3c. You are given the mean of 20.3 for a random sample of 90 observations from a normal distribution population with a standard deviation of 3.9. Construct a 95% confidence level and interpret your answer. [3]
You are given the following information of a company that produces cola fizzy drinks. The
company states that the mean caffeine content per bottle of a fizzy drink is 40 mg with a
standard deviation of 7.5 mg. The quality controller is convinced that it is lower. A sample of
30 randomly drawn bottles has a mean caffeine content of 39.2 mg. Can the quality
controller reject the claim? Conduct a hypothesis test at 0.05 level of significance.
In a recent survey, a researcher claimed that the average life expectancy of people in a certain country is 72 years. Is his claim correct if a random sample of 25 deaths from his country showed a mean of 71.2 years with standard deviation of 1.2 years? Use 99% confidence level.
A bank manager wants to know the mean amount of mortgage paid per month by
homeowners in an area. A random sample of 120 homeowners selected from this area
showed that they pay an average of R6500 per month for their mortgages. The
population standard deviation of such mortgages is R1500.
i. Identify the point estimate for the average monthly mortgage amount. [1]
ii. Explain the significance of a confidence interval in this regard – in other words, why
is it not correct (not recommended) to say that the average amount of mortgage paid by all homeowners is R6500?
What is the appropriate distribution to use? Explain. [2]
Find a 99% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. Interpret the results. [5]
What effect would a change from a 99% to a 90% confidence level have on the interval width for the average mortgage amount? Explain. [3]
Among 157 African-American men, the mean systolic blood pressure was 146 mm
Hg with a standard deviation of 27. We wish to know if on the basis of these data,
we may conclude that the mean systolic blood pressure for a population of African-
American is greater than 140.
• Setup the null and alternate hypothesis (1 mark)
• Determine the type of the test (1 mark)
• Use α=0.01, conduct the test and accept or reject the hypothesis on the basis of
the test. (Given Z_0.99=2.33) (3 marks)
The average number of homes sold by a realty company is 2 homes per day. What is the probability that exactly 3 homes will be sold in the next Sunday.( Given that e=2718)
y'' - 3y' - 10y = 0 ; y(0)=1 and y'(0)=10
Directions: Read job vacancies posts on the classified ads section of a newspaper. Then, draw conclusions about the type of people who will apply for each job. Write your conclusions based on facts and include newspaper clippings where you got the information. You will be graded using the given rubric below.
Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. z^2=4+4r^2
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#340153 on Dec 2023