Mathematics-IV Unit 5 Notes AKTU (BAS303)

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Unit 5 · Notes

AKTU Mathematics-IV (BAS303) Unit 5 notes for B.Tech Semester 3/4 – Statistical Techniques III. Topics: Sampling Theory and Hypothesis, Statistical Tests of…

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Unit 5: Statistical Techniques III – AKTU syllabus topics

  • Sampling Theory and Hypothesis: Null and Alternative Hypothesis, Level of Significance Confidence
  • Statistical Tests of Significance: t-Test, Z-Test, Chi-Square Test
  • Statistical Quality Control: X-bar and R Control Charts, p np and C Charts

Most asked AKTU PYQ questions from Unit 5

  1. Q7a. Two independent samples of 8 and 7 items respectively had the following values of the variables: Sample I: 9 11 13 11 15 9 12 14, Sample II: 10 12 10 14 9 8 10. Is the difference between the means of the sample significant? (7 marks, 2024-25)
  2. Q2e. From the following table regarding the color of eyes of father and son, test if the color of son's eye is associated with that of father. Eye color of father / Eye color of son — Light/Light: 471, Light/Not Light: 51, Not Light/Light: 148, Not Light/Not Light: 230. Given 𝜒²₀.₀₅(1) = 3.841 (10 marks, 2020-21)
  3. Q7b. Distinguish between the np-chart and p-chart. Following is the data of defective of 10 samples of size 100 each. Construct np chart and examine whether the process is in statistical control? Sample no.: 1 2 3 4 5 6 7 8 9 10, No. of defectives: 6 9 12 5 12 8 8 16 13 7 (10 marks, 2020-21)
  4. Q7b. By using Chi-square test, find whether there is any association between income level and type of schooling: Income vs Public school / Govt. School: Low: 200, 400; High: 1000, 400. (7 marks, 2024-25)
  5. Q7a. The height of 6 randomly chosen sailors in inches are 63, 65, 68, 69, 71 and 72. Those of 9 randomly chosen soldiers are 61, 62, 65, 66, 69, 70, 71, 72 and 73. Test whether the sailors are on the average taller than soldiers. (7 marks, 2023-24)
  6. Q1j. Explain the t-test for small samples. (2 marks, 2020-21)
  7. Q7a. The values in two random samples are given below: Sample 1: 15 25 16 20 22 24 21 17 19 23, Sample 2: 35 31 25 38 26 29 32 34 33 27 29 31. Can we conclude that the two samples are drawn from the same population? Test at 5% level of significance. (10 marks, 2022-23)
  8. Q2e. The score of 10 candidates obtained in tests before and after attending coaching classes: Before: 54 76 92 65 75 78 66 82 80 78, After: 60 80 86 72 80 72 66 88 82 73. Is the coaching for the test effective? Test at 5% level of significance. (10 marks, 2022-23)
  9. Q7a. The demand for a particular spare part in a factory was found to vary from day to day: Days: Mon Tue Wed Thu Fri Sat, No. of parts demanded: 1124 1125 1110 1120 1126 1115. Use χ²-test to test the hypothesis that the number of parts demanded does not depend on the day of the week. [χ²₀.₀₅ = 11.07… (10 marks, 2021-22)
  10. Q7b. Following is the data of defectives of 10 samples of size 100 each. Sample no: 1-10, No. of defectives: 15 11 9 6 5 4 3 2 7 1. Construct p-chart and state whether the process is in statistical control. (10 marks, 2021-22)

AKTU paper codes: BAS303, BAS303H, BAS403, BAS403H, KAS302, KAS402

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