Which of the following statements are true? Give reasons for your answer.
(i) F-distribution is always used in goodness of fit.
(ii) Measure of central tendency in a data set refers to the extent to which the observations are scattered.
(iii) A process is said to be under assignable cause when the points are above the VCL link of () chart.
(iv) Simple random sampling is done by using random number tables where the probability of drawing a digit is 0⋅ 1.
(v) All time series have a trend.
(i) False. F-distribution is not used in goodness of fit tests; it is primarily used to compare variances between two samples, such as in ANOVA (Analysis of Variance). The Chi-square distribution is commonly used for goodness of fit tests. (ii) ________ _____ _____ ____ ______ _____ _________ _______ _______ _________ _______ __________.
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Plating of gold on wrist watches requires a chemical called AiCl3. Concentration of the chemical that is added to the solution is an important factor. The objective is to choose that concentration for which plating is uniform. Three concentration of AiCI3 chosen were 5%, 15% and 20%. These were added in the solution and plating was done and thickness (in units) measured on 5 samples is gives below.
| Sample → ------------------------- ↓ Conc. of | 1 | 2 | 3 | 4 | 5 |
| 5% | 3 | 2 | 4 | 2 | 4 |
| 15% | 4 | 4 | 3 | 2 | 4 |
| 25% | 3 | 3 | 4 | 4 | 2 |
Use ANOVA to comment on whether the concentration of AiCI3 gives same result or 3 not. (Use )
Write three advantage and three disadvantage of using a sampling approach instead of a census approach for studying a characteristic.
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नीचे 10 छात्रों द्वारा भौतिकी और गणित में (25 में से) प्राप्त किए गए अंकों का बंटन दिया गया है :
क्रम सं.
| भौतिकी (Xi ) | गणित (Yi ) |
|
|
| |
| 1 | 18 | 21 | 324 | 441 | 378 |
| 2 | 20 | 23 | 400 | 529 | 460 |
| 3 | 11 | 14 | 121 | 196 | 154 |
| 4 | 20 | 23 | 400 | 529 | 460 |
| 5 | 14 | 17 | 196 | 289 | 238 |
| 6 | 15 | 18 | 225 | 324 | 270 |
| 7 | 13 | 16 | 169 | 256 | 208 |
| 8 | 16 | 19 | 256 | 361 | 304 |
| 9 | 17 | 20 | 289 | 400 | 480 |
| 10 | 20 | 23 | 400 | 529 | 460 |
| कुल जोड़ | 164 | 194 | 2780 | 3854 | 3412 |
Consider the case of tossing two dices. Let
A : be the event of getting an odd total
B : the event of getting on the first dice, and
At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in weeks:
| Time | Sample number | ||||
| 1 | 2 | 3 | 4 | 5 | |
| 9 am: | 8 | 9 | 15 | 4 | 11 |
| 10 | 7 | 10 | 7 | 6 | 8 |
| 11 | 11 | 12 | 10 | 9 | 10 |
| 12 | 12 | 8 | 6 | 9 | 12 |
| 1 p.m. | 11 | 10 | 6 | 14 | 11 |
| 2 | 7 | 7 | 10 | 4 | 11 |
| 3 | 10 | 7 | 4 | 10 | 10 |
| 4 | 8 | 11 | 11 | 11 | 7 |
Compute the control limits for and R--charts. Draw the control charts for
and ,R and comments.
Two cards are drawn simultaneously or successively without replacement from a well-shuffled deck of 52 cards. Find the probability distribution of number of aces (x). Give a graphical representation of probability distribution.
Which of the following statements are true? Give reasons for your answer.
(i) F-distribution is always used in goodness of fit.
(ii) Measure of central tendency in a data set refers to the extent to which the observations are scattered.
(iii) A process is said to be under assignable cause when the points are above the VCL link of () chart.
(iv) Simple random sampling is done by using random number tables where the probability of drawing a digit is 0⋅ 1.
(v) All time series have a trend.