Question

Q1(a). The pulse rate for the patients are given below: 62, 72, 66, 79, 83, 61, 62, 85, 72, 64, 74, 71, 42, 38, 91, 66, 77, 90, 74, 63, 64, 68, 42 Find mean, median, mode, range and standard deviation of the above data set. If we decrease the pulse rate by a fixed number, describe its effect on mean and standard deviation 5 Marks Q1(b) (). A survey of 50 first-time Scuba divers showed that 23 did not want to repeat the experience. Find the 90% confidence interval of the true proportion of divers who did not wish to dive a second time. If a diving company wants to distribute brochures for repeat diving, what is the minimum number it should print? 3 Marks (11) ICT wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if ICT wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours? 2 Marks Q2(a) (). In the past, 20% of all airline passengers flew first class. In a sample of 15 passengers, 5 flew first class. At a = 0.10, can you conclude that the proportions have been changed? 3 Marks (ii). Give your comments on the use of one-tail and two-tail test with a suitable example. 2 Marks Q206) (). Fifty percent of new electricians have had diploma education. During their first year, new electrician without education has probability 0.08 of having an accident, but new electrician with education has only a 0.05 probability of an accident. What is the probability a new electrician has had diploma education, given that the electrician has had no accident the first year? 3 Marks (1). The Mathematics Department of the University of Nizwa consists of 8 professors, 6 associate professors, 13 assistant professors. In how many of all possible samples of size 4 chosen without replacement, will every type of professor be represented? 2 Marks

Answer 1

Question 1: (a)

mean	68.09
sample standard deviation	13.95
median	68.00
mode	62.00
range	53

The mean and standard deviation will remain the same.

(b) (i) The 90% confidence interval is between 0.3441 and 0.5759.

Observed
0.46	p (as decimal)
23/50	p (as fraction)
23.	X
50	n
0.0707	std. error
0.3441	confidence interval 90.% lower
0.5759	confidence interval 90.% upper
0.1159	margin of error

(ii) n = (2.576*6.2/1.5)2

n = 114