Productivity is the key driver of wages and one of the most important determinants of living standards. The British Chambers of Commerce commissioned research into understanding whether labour productivity in the automotive manufacturing sector in England and Ireland were the same or different. The researchers collected data on a random sample of 8 firms in England and 4 in Ireland and recorded productivity in units of value added (£) per hour. It is assumed that firm-level productivity has a normal distribution. The following data were collected: Ireland 47 56 43 68 England 39 50 39 45 50 43 35 43 (i) Set up appropriate null and alternative hypotheses and conduct a test of the hypotheses of equal mean productivity in Ireland and England at 5 per cent significance level under the assumption of unknown but equal population variances. Provide as much detail as possible on your procedures. Clearly show all your steps in testing and state your decision. Discuss the economic implications of your findings. Do you think the assumption of equal population variances is justified? (ii) Now conduct the test assuming unknown and potentially unequal variances between firms in Ireland and England. Clearly write down your null and alternative hypotheses, assumptions, the test statistic, and its sampling distribution. Conduct the test and discuss your findings. How do the results compare with the previous case? Discuss.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Productivity is the key driver of wages and one of the most important
determinants of living standards. The British Chambers of Commerce
commissioned research into understanding whether labour productivity in the
automotive manufacturing sector in England and Ireland were the same or
different. The researchers collected data on a random sample of 8 firms in
England and 4 in Ireland and recorded productivity in units of value added (£)
per hour. It is assumed that firm-level productivity has a normal distribution.
The following data were collected:
Ireland 47 56 43 68
England 39 50 39 45 50 43 35 43
(i) Set up appropriate null and alternative hypotheses and conduct a test of
the hypotheses of equal mean productivity in Ireland and England at 5 per

cent significance level under the assumption of unknown but equal
population variances. Provide as much detail as possible on your
procedures. Clearly show all your steps in testing and state your decision.
Discuss the economic implications of your findings. Do you think the
assumption of equal population variances is justified?

(ii) Now conduct the test assuming unknown and potentially unequal variances

between firms in Ireland and England. Clearly write down your null and
alternative hypotheses, assumptions, the test statistic, and its sampling
distribution. Conduct the test and discuss your findings. How do the results
compare with the previous case? Discuss.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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