Quan1102 Statistics | Compute Assessment Answer

Question 1

(a) Explain the different types of sampling techniques

Question 2

(a) (i)The temperature in a city is a random variable having a normal distribution with mean 25°C and standard deviation of 3°C. What is the probability that on a particular day, the temperature is 

(1) More than 29°C 

(2) Less than 23°C 

(3) Between 24°C and 27°C

(b) (i) A random sample of 81 households in a town was selected and the mean electricity usage was found to be 425 KWH and standard deviation of 72 KHW. Calculate the 98% confidence interval for the mean electricity usage of households in that town.

(ii) Compute the 98% confidence interval if in another town, a sample of 14 households revealed that the mean of electricity usage, which is assumed to be normally distributed, was 518 KWH and standard deviation of 54KWH.

Question 3

(a) What are the assumptions associated with the simple linear regression model?

(b) In a laboratory, the observation carried out on a sample of mice revealed their body weight (X) and their heart weight (Y) as follows:

Body weight (g)       30   37   38   32    36   38   42    36    41

Heart weight (mg) 119  136 140  123  131 136 145 135 142

(i) Draw a scatter diagram of the given data on graph paper and comment on the relationship between the body weight and the heart weight of the mice. (4 marks)

(ii) Find the equation of the estimated least squares regression line of y = a + bx and plot the line on the same graph as the scatter diagram. Interpret the values of a and b in your least squares regression line. 

(iii) Calculate the correlation coefficient and the coefficient of determination. State what do they indicate about the relation between body weight and the heart weight of mice. 

(iv) Estimate the likelihood of weight of the heart when the body weight of a mouse is:

(1) 33 grams

(2) 25 grams