QSCI 381 Practice final

 

#1. In each of the following ten statements respond with true or false, giving reasons for your response.

a) Size classes: 6-8, 9-11, 12-14, etc imply that the class interval is 2 units.

b) In positively skewed data the median is larger than the mean. .

c) If the standard deviation in population A is larger than in B, the coefficient of variation in A must also be larger than in B.

d) If two events are independent, they can not be mutually exclusive.

e) In a test of hypothesis, the probability of committing type I error increases with increase in the significance level.

f) The regression coefficient b (of ) must be large if the covariance (Sxy) is large.

g) If the null hypothesis is rejected in a one-tailed test for a given significance level, it will certainly be rejected in a two-tailed test.

h) For given population variance (s 2), confidence level (1-a ),and the margin of error (E), the sample size needed will be halved if the population size is reduced to half of its original size.

i) The sample variance (S2) decreases with increase in the sample size.

j) In the chi-square test for equality of two or more proportions, doubling of all frequencies will result in quadrupling of the chi-square statistic.

#2. a). The sex-ratio in spotted owls is said to be 5 males to every 10 females. In order to test this hypothesis 32 spotted owls were randomly trapped out of which 6 were males. Set up appropriate null and alternate hypotheses, and test at 0.05 level of significance if the null hypothesis is tenable.

b). Would there be any difference in the test results if we had observed 12 males in a random sample of 64 spotted owls? Explain.

#3. a) The lengths of a certain larvae are normally distributed with s = 4.0. If 84.13% of these larvae are 59 mm or smaller, what fraction of the larvae are between 51mm and 63 mm in length?

b) If we take a random sample of 25 larvae from the population in #3.a) above, what is the probability that the difference between the sample mean and the population mean will not be more than 1 mm?

c) How large should the random sample be, if want the difference between the population and sample mean to exceed 1 mm with a probability of no more than 0.05?

#4 Members of a group containing two shorebird species were observed to distribute themselves as follows while feeding. Test at 0.05 significance level, the null hypothesis that the members of the two species utilize the same feeding locations.

Species

In water

In wet mud

In dry mud

Total

1

39

104

31

174

2

48

294

162

504

Total

87

398

193

678