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It is believed that there is a relationship between ‘level of information’ and ‘readiness to take a vaccination jab’ among tertiary institution students. To test this relationship, a research team decides to conduct a study using a sample of tertiary students.
Level of information
Readiness score
7
7
9
6
9
6
2
3
8
9
5
7
7
6
6
7
8
6
10
9
a. Use the data supplied in a table to manually calculate the correlation coefficient (r). Show all your calculations. (14 Marks)
b. What does the ‘correlation coefficient’ that you calculated tell you about the direction and strength (magnitude) of the relationship between information and readiness? (3 Marks)
c. Calculate and interpret the coefficient of determination for this relationship. (3 marks)
In a study of obesity the following results were obtained from samples of males and females between the ages of 20 and 75:
n No. Overweight
Male 150 21
Female 200 48
Can we conclude from these data that in the sampled populations there is a difference in the proportions who are overweight? Let α=0.05
A company has purchased a plant that must be installed and commissioned in 7 to 10 days by a services firm. The following table shows the services firm’s probability assessment for the number of days required to install and commission the plants from past experiences. Number of days 2 5 6 7 8 Probability 0.09 0.25 0.31 0.26 0.09 Let A be the event “the plant will be installed and commissioned in more than 6 days,” and let B be the event “the machinery will be installed and commissioned in less than 7 days” a. Find the probability of event A. b. Find the probability of event B. c. Find the probability of the complement of event A. d. Find the probability of the intersection of events A and B. e. Find the probability of the union of events A and B.
A random sampleY1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density function is given by: f (Y ) = βe − βY , Y 0 & β > 0 a). Obtain the maximum likelihood estimator (MLE) of β. (3 points) 1Econometrics- Assignment I b). Given that ∑ n Y i = 25 , ∑n Yi 2 = 50 , n = 50 calculate the maximum likelihood i =1 i =1 estimate of β. (3 point) c). Using the same data as in part (b), test the null hypothesis that β =1against the alternative hypothesis that β ≠1at 5% level of significance
Problem 5 Show that the test taking the overall significance of regression model using ANOVA table to be expressed as: 𝑭 = 𝑹 𝟐⁄𝒌 − 𝟏 (𝟏 − 𝑹𝟐)⁄𝒏 − 𝒌 Where, R be a level of determination and k is the number of parameters in the n sampled regression model. (3 points
Problem 3 In this question we look at the relation between the logarithm of weakly earnings and years of education. Using data from the national longitudinal study of youth, we find the following results for a regression of log weekly earnings and years of education, experience, experience squared and an intercept:Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2 ( 0.222) ( 0.008) ( 0.025) (0.001) a).Construct a 95% confidence interval for the effect of years of education on log weakly earnings. (2 point) b).Consider an individual with 10 year of experience. What would you expect to be the return to an additional year of experience for such an individual (the effect on log weakly earnings)? (3 point) c).
A company has purchased a plant that must be installed and commissioned in 7 to 10 days by a services firm. The following table shows the services firm’s probability assessment for the number of days required to install and commission the plants from past experiences. Number of days 2 5 6 7 8 Probability 0.09 0.25 0.31 0.26 0.09 Let A be the event “the plant will be installed and commissioned in more than 6 days,” and let B be the event “the machinery will be installed and commissioned in less than 7 days” a. Find the probability of event A. b. Find the probability of event B. c. Find the probability of the complement of event A. d. Find the probability of the intersection of events A and B. e. Find the probability of the union of events A and B
A pair of fair dice is tossed one time. What is the probability that ⦁ The sum of two faces is a prime number? ⦁ The sum of two faces is more than 9? ⦁ The sum of two faces is between 5 and 9? ⦁ The sum of two faces is at most 6? ⦁ The sum of two faces is at least 8?
From a batch containing 4 boys and 6 girls, a group of 4 students is to be selected. There are how many combinations of ⦁ 2 boys and 2 girls. ⦁ 3 boys and 1 girl. ⦁ 4 boys. ⦁ At least 2 boys Assignment expert
How many 3 digits numbers are possible using the digits 0, 1, 2, 3, 4 each digit using only once.
⦁ Numbers are odd.
⦁ Numbers are even.
