Question:
(a) A normal distribution is thought to have a mean of 50. A random sample of 100 gave a mean of 52.6 and a standard deviation of 14.5. A significance test was carried out at the 5% level to verify an increase in the population mean. By letting the population mean to be µ and population variance to be , σ^{2}
(i) formulate the hypothesis for the problem,
(ii) calculate a 95% confidence interval for µ.
Using the standard test statistic the null hypothesis is rejected at the 5% level of confidence.
(iii) Explain what is meant here, paying particular attention to the level of significance.
(iv) What would be your conclusion at the 10% level of significance?
(b) During an experiment the following data is collected from a sample of size 15,
10,13,12,14,8,11,7,19,21,18,17,16,14,13,13
Determine the best estimates of the population mean and variance.
(c) A company manager wanted to predict the production cost( ), in thousand of rupees, of an item by the number of items produced (y
x ), in thousands. A least squares regression model of the form x y 966 . 0 1 . 20 + = is obtained based on available data.
(i) Use the model to estimate the production cost when x = 69.
(ii) Given that x = 42.147, calculate y.
(iii) Interpret the coefficient of x.
(iv) The correlation coefficient, r = 0.997. Conclude on the relationship between x and y.