Q1. A nonparametric test

does not need a null hypothesis
does not need data to be numerical measurements
can use ranked data
can be one-tail or two-tail
usually tests medians instead of means.

Q2. In acceptance sampling,

producer's risk is similar to Type I error
consumer's risk is similar to Type II error
the consumer has a small probability of accepting a poor       batch of material
producer's risk is equal to consumer's risk
the producer suffers a small probability of a good batch being rejected.

Q3. A probability density function f(x)

can be used to model a continuous variate
integrates to 1 over the range of x
increases steadily from 0 to 1
must be greater than or equal to 0 over the range of x
can be defined over a range of x including both positive and negative values.

Q4. A continuous random variable has the probability density function f(x) = 1/3, for x between – 1 and +2, and 0 elsewhere. Its mean, variance and median are:

(1, ¾, ½)
(½, ¾, ½)
(1½, 1, 0)
(½, 1, 1½)
(½, ¾, 1)

Q5. The standard deviation of the random variable X whose probability density function is
f(x) = kx(4 – 3x) between x = 0 and 1 is

0.244
0.632
0.060
0.400
0.583

 

Q6. The median of an exponential distribution whose mean is 3 is:

0.48
4.33
3.00
0.23
2,08

Q7. The random variable X has a normal distribution with mean 5.75 and variance 2.56. The probability that X lies between 5.5 and 6.5 is

0.438
0.118
0.242
0.320
0.167

Q8. In a production process there are three phases P, Q, R, carried out one after the other without delay. The times (minutes) taken for these follow independent normal distributions, with means and variances (8, 9) for P, (6, 4) for Q and (11, 3) for R. The probability that an item from this process takes more than 30 minutes to produce is:

0.229
0.106
0.584
0.416
0.212

Q9. The time (minutes) taken to reach working temperature after a piece of machinery is switched on follows a normal distribution. The probability of taking more than 5 minutes is least when the mean and variance are:

(4.0, 0.25)
(3.0, 0.87)
(3.7, 0.33)
(3.3, 0.64)
(4.3, 0.12)

Q10.A normally distributed random variable is thought to have mean 7. Its variance is assumed to be 5. The mean of a random sample of n observations from this distribution is 6.28, and is used to test the null hypothesis “µ = 7”. The result of the test is just on the borderline of significance at the 5% level in a two-tail test. The sample size n is:

7
14
22
31
37

Q11. Two sports clubs run three teams each, first, second and youth. At the end of a season Club L’s teams have won 65 out of 110 games and Club M’s teams have won 42 out of 96 games. The standard error of the difference between the proportions of games won is:

0.069
0.051
0.047
0.049
0.091

Q12. In hypothesis testing, a normal approximation may NOT be used for

a chi-squared distribution with 20 degrees of freedom
a t-distribution with 58 degrees of freedom
a proportion based on a sample of 350 observations
a mean of 225 measurements
a Wilcoxon signed-rank test based on 30 pairs of data.

Q13. Two independent random samples are drawn from normal distributions with means µ1, µ2 and the same variance s2, which is not known. One sample, consisting of 8 observations, has mean 24.25 and the standard error of the mean is 2.031. The other sample, consisting of 12 observations, has mean 27.33 and the standard error of the mean is 1.555. The degrees of freedom and the p-value for a two-tail test of the Null Hypothesis “µ1 = µ2” are

(20, 0.88)
(18, 0.24)
(19, 0.24)
(18, 0.88)
(18, 0.12)

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