Statistics · 3rd secondary · First Term

Normal Distribution — Estimation and confidence intervals

About this lesson

This unit introduces the concepts of point estimation and interval estimation for a population mean. It defines a parameter as an unknown constant characterizing a population, and estimation as a statistic from a sample that approximates this parameter. The unit focuses on interval estimation, explaining the confidence interval as a range of values expected to contain the population parameter with a certain probability, and the level of confidence as the probability (1 - α) that the interval contains the true parameter. It demonstrates how to find the critical value Z(α/2) from the standard normal distribution table for given confidence levels, such as 95% and 99%. The estimation error E is defined as E = (σ/√n) × Z(α/2), and the confidence interval for the population mean is given as [X̄ - E, X̄ + E]. Worked examples and exercises apply these formulas to scenarios like pulse rates, test scores, working hours, and bill values, using sample means, standard deviations, and sample sizes to compute intervals and interpret them. By the end, students should be able to calculate the critical value, estimation error, and confidence interval for a population mean, and interpret the meaning of a confidence interval.

Main topics in this lesson

  • Point estimation
  • Interval estimation
  • Confidence interval
  • Critical value
  • Estimation error
  • Confidence level

Key terms and vocabulary

  • Parameter
  • Point Estimate
  • Interval Estimation
  • Confidence Interval
  • Level of Confidence
  • Critical Value
  • Estimation Error
  • Lower Bound
  • Upper Bound

Questions and answers on Normal Distribution — Estimation and confidence intervals - practice and revision

Multiple choice questions on this lesson in Statistics for 3rd secondary, First Term, with practice exercises for revision and exam preparation.

1

إذا كان X̄ = 100 و σ = 20 و n = 100 و Z(α/2) = 2.58 فإن فترة الثقة للمتوسط هي:

  • 1 [94.84, 105.16]
  • 2 [94.84, 100]
  • 3 [100, 105.16]
  • 4 [95, 105]
2

إذا كان X̄ = 100 و σ = 20 و n = 100 و Z(α/2) = 1.96 فإن فترة الثقة للمتوسط هي:

  • 1 [96.08, 103.92]
  • 2 [96, 104]
  • 3 [100, 103.92]
  • 4 [96.08, 100]
3

إذا كان σ = 10 و n = 100 و Z(α/2) = 2.58 فإن خطأ التقدير E يساوي:

  • 1 2.58
  • 2 25.8
  • 3 0.258
  • 4 258
4

إذا كان σ = 10 و n = 100 و Z(α/2) = 1.96 فإن خطأ التقدير E يساوي:

  • 1 1.96
  • 2 19.6
  • 3 0.196
  • 4 196
5

فترة الثقة هي:

  • 1 مدى من القيم يُتوقع أن يحتوي على معلمة المجتمع باحتمال معين
  • 2 قيمة واحدة تقدّر المعلمة
  • 3 ثابت مجهول يميز المجتمع
  • 4 إحصاء من العينة
6

مستوى الثقة هو:

  • 1 الاحتمال (1 - α) أن تحتوي الفترة على المعلمة الحقيقية
  • 2 الاحتمال α أن لا تحتوي الفترة على المعلمة
  • 3 القيمة الحرجة Z(α/2)
  • 4 خطأ التقدير E

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