Question

Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken.Suppose that at one firm, it is known that over the past years employees have taken a mean of 4.5 sick days.This year, the firm introduces telecommuting.management chooses a simple random sample of 90 employees to follow in detail and at the end of the year ,these employees average 4.3 sick days with a standard deviation of 2.2 days. Let μ represent the mean number of sick days for all employees of the firm.management wants to find out the effect of this method and wants to test

null Hypothesis H0 : μ ≥ 4.5 versus alternative hypothesis H1 : μ < 4.5

a)For this testing ,calculate the z-score(test statistic) for the observed mean value of 3.4 sick days.

b)Hence find the p-value for the test.

c)Draw the normal curve and colour the region equal the p-value, clearly making test statistic (z-score) on the diagram.

D)Does the management convince that it is less than 4.5 days of statistically significant at 1%? explain

Answer 1