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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Consider a population of 11 schools from which a sample of size 3 is to be selected. List all the possible samples by circular systematic sampling.
) In a television appearance, an MLA from a state asks voters in that state to indicate whether the MLA should vote against or for a particular piece of legislation. The MLA office receives 4100 replies. Since voters from western part tends to be democrats while those from eastern parts tend to e communists, the MLA divides the replies on the basis of their geographical origin. 68% of the replies from the western part are against the legislation and 36% of the replies from the eastern part are against it.
(i) Did the MLA carry out a stratified sampling?
(ii) Did the MLA carry out a stratified random sampling?
(iii) How would you justify the sample design?
(iv) What improvements would you suggest?
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 )
हाथ की घड़ियों पर सोने का पानी चढ़ाने के लिए AiCl3. नामक रासायनिक पदार्थ का प्रयोग किया जाता है। घोल में रसायन के सांद्रण का पता होना आवश्यक होता है। हमारा उद्देश्य एक ऐसे सांद्रण का प्रयोग करना है, जिससे कि सोने का लेपन एकसमान रूप से हो सके। चुने हुए तीन AiCl3 के सांद्रण 5%, 15% और 20% थे। इन्हें घोल में मिला दिया गया और इससे लेपन किया गया और नीचे दिए गए 5 प्रतिदर्शों पर इनकी मोटाई (इकाई में) मापी गई जो कि निम्न है :
| प्रतिदर्श → ------------------------- ↓ का सांद्रण | 1 | 2 | 3 | 4 | 5 |
| 5% | 3 | 2 | 4 | 2 | 4 |
| 15% | 4 | 4 | 3 | 2 | 4 |
| 25% | 3 | 3 | 4 | 4 | 2 |
AiCl3 के सांद्रण से समान परिणाम प्राप्त होते हैं या नहीं, इस पर टिप्पणी देने के लिए ANOVA (यहाँ का प्रयोग कीजिए)
(ख) 11 विद्यालयों की एक समष्टि लीजिए जिससे साइज 3 के एक प्रतिदर्श का चयन करना है। वृत्तीय व्यवस्थित प्रतिचयन से सभी संभव प्रतिदर्शों की सूची बनाइए।
A manufacture of rayon wants to compare that the yield strength of 11⋅5 kg/ mm2 is met or not at 5% level of significance. The manufacturer draws a sample and calculates the mean to be 12⋅8kg/ mm2 and the standard derivation is known to be 2⋅0kg/ mm2 . Carry out the statistical test appropriate for this.
b) A box contains 10 screws, 3 of which are defective. Two screws are drawn at random. Find the probability that none of them is defective, if the sample is drawn
(i) with replacement,
(ii) without replacement.
c) A researcher measures the temperature of a solution 5 times. The observations are 25, 32, 27, 29, 30 o C. Determine an unbiased estimate of the temperature.
एक बॉक्स में 10 पेंच हैं, जिनमें से 3 खराब हैं। इसमें से यादृच्छिक रूप से 2 पेंच निकाले जाते हैं। इसकी प्रायिकता ज्ञात कीजिए कि इनमें से कोई भी पेंच खराब नहीं होगा, यदि प्रतिदर्श
(i) प्रतिस्थापन के साथ निकाला जाता है,
(ii) बिना प्रतिस्थापन के निकाला जाता है।
ग) एक अनुसंधानकर्ता एक घोल का तापमान पाँच बार मापता है। प्रेक्षण हैं। तापमान का एक अनभिनत आकल ज्ञात कीजिए।
Write three advantage and three disadvantage of using a sampling approach instead of a census approach for studying a characteristic.