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 )
For the three concentrations the observed thickness values are 5% : 3, 2, 4, 2, 4 15% : 4, 4, 3, 2, 4 25% : 3, 3, 4, 4, 2 First find totals and means. For 5% : total = 3+2+4+2+4 = 15, mean = 15/5 = 3 For 15% : total = 4+4+3+2+4 = 17, mean = 17/5 = 3.4 For _____ ________ _______ ________ __________.
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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 )
In a locality of 18,000 families, a random sample of 840 families was taken. Of these 840 families, 206 families were found to have a monthly income of Rs. 500 or less. Give the confidence interval for the families having income Rs. 500 or less.
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।
Two samples of 9 and 8 sizes give the sum of squares of deviations from respective means equal to 160 and 91 inches squares. Test whether these samples have been drawn from same normal population or not? (Use )
Find and
.
Check whether A,B and C are independent or not. Give reasons for your answers.
It is desired to estimate average annual wool yield per sheep for a herd of 150 at a certain farm house using stratified simple random sampling. Sheeps in the herd are to be grouped into three strata on the basis of first shaving in days. Optimum method sample allocation is said to be used for selecting the overall sample of 25 sheeps from the three strata. Determine approximately optimum strata boundaries using the information on first shaving given below.
| having days | No. of Sheep (f) |
|
| 30-70 | 6 | 2.45 |
| 70-110 | 2 | 1.414 |
| 110-150 | 1 | 1 |
| 150-190 | 4 | 2 |
| 190-230 | 2 | 1.414 |
| 230-270 | 7 | 2.646 |
| 270-310 | 8 | 2.828 |
| 310-350 | 20 | 4.472 |
| 350-390 | 10 | 3.162 |
| 390-430 | 25 | 5 |
| 430-470 | 40 | 6.325 |
| 470-510 | 25 | 5 |
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.
स्तरित सरल यादृच्छिक प्रतिचयन का प्रयोग करके एक फार्म हाउस पर 150 भेड़ों के झुंड से प्रति भेड़ ऊन का औसत वार्षिक उत्पादन का आकलन ज्ञात करना है। इसके लिए झुंड के भेड़ों को दिन में प्रथम शेविंग के आधार पर तीन स्तरों में वर्गीकृत करना होता है। यह माना जाता है कि तीन स्तरों से 25 भेड़ों के समग्र प्रतिदर्श का चयन करने के लिए प्रतिदर्श-नियतत की इष्टतम विधि का प्रयोग किया जाता है। निम्नलिखित प्रथम शेविंग पर प्राप्त सूचना के आधार पर सन्निकटतः इष्टतम स्तर परिसीमाएँ ज्ञात कीजिए :
| शेविंग दिन | भेड़ों की संख्या (f) |
|
| 30-70 | 6 | 2.45 |
| 70-110 | 2 | 1.414 |
| 110-150 | 1 | 1 |
| 150-190 | 4 | 2 |
| 190-230 | 2 | 1.414 |
| 230-270 | 7 | 2.646 |
| 270-310 | 8 | 2.828 |
| 310-350 | 20 | 4.472 |
| 350-390 | 10 | 3.162 |
| 390-430 | 25 | 5 |
| 430-470 | 40 | 6.325 |
| 470-510 | 25 | 5 |