Statistics and Probability Answers

A market research study is to be conducted among users of a particular type of computer system. How many users should be sampled to estimate the percentage of users who plan to add terminals to within 5 percentage points with 97% confidence?

A low-noise transistor for use in computing products is being developed. It is claimed that the mean noise level will be below the 3.00 dB level of products currently in use. (Assume that noise level is normally distributed).
i. Set up the appropriate null and alternative hypotheses for verifying the claim.
ii. Find the critical point for 99% confidence test based on a sample of size 20. Using the values 2.2 and 0.88 of sample mean and sample standard deviation, respectively, to test null hypothesis against alternative hypothesis defined in (i) at  = 0.01. Justify.

Sachin Tendulkar scores runs in T-20 league match with following discrete probability density function.
Runs (X) 50 35 25 15 45 10
f(x) 0.10 0.18 0.20 0.25 0.12 0.15



Simulate the score of Sachin Tendulkar for four league matches using following three digit random numbers 976, 009, 280, and 850. Hence estimate his average score.

For a given data set
x 5 15 25 35 45 50
y 10 18 20 25 32 45
i. Find the value of , and
ii. Write the normal equations and estimate the equation of line of regression of Y on x.
iii. Find the value of sample correlation coefficient for the above data.

The joint density function for continuous random variable (X, Y) is given by

Find
(a). P[0<=X+Y<=1]
(b). Find marginal densities for X and Y respectively. Are X and Y independent random variables? Justify your answer.
(c).

Metal conduits or hollow pipes are used in electrical wiring. In testing 1-inch pipes, these data are obtained on the outside diameter (in inches) of the pipe: 1.21, 1.19, 1.20, 1.22, 1.18, 1.23, 1.17, 1.09. Assume that sampling is from normal distribution with mean and variance .
i.Find unbiased estimates for and .
ii.Find 95% confidence interval on the mean outside diameter of pipes of this type.

Suppose that, on average, 1 person in 1000 makes a numerical error in preparing his or her income tax return. If 10,000 forms are selected at random and examined, find the probability that at most 2 of the forms contain an error.

True or False. Justify
If a sample of 20 cancer patients from oncology departments of Govt.
Hospitals is to be taken , then the sample technique used is simple random
sampling.

True or False. Justify
If a control chart shows that the points are very close to the central line, then the process is in control.

True or False. Justify
If two events A and B are mutually exclusive, they are not dependent.