Question

Here are summary statistics for randomly selected weights of newborn girls: n= 153, x= 32.2 hg, s= 7.6 hg. Construct a confidence interval estimate of the mean. Use a 90% confidence level. Are these results very different from the confidence interval 31.2 hg<x<34.2 hg with only 15 sample values, x= 32.7 hg, and s= 3.3 hg? What is the confidence interval for the population mean? hg<u< hg (Round to one decimal place as needed.)

Answer 1

• The given information are:
  
  T= 32.2
  
  
  n = 153
  
  
  S = 3.3
  
  
  The 90% Confidence Interval is given by:
  
  S (T-- n * tm-10.05 , T + tn-10.05 ) 12 이녁
  
  Now,
  
  t152;0.025 1.65494
  
  Putting in the given values, we get,
  
  3.3 (32.2- * 3.3 1.65494, 32.2+ * 1.65494) V153 V153
  
  
  (31.7584799, 32.6415201
  
  
  (31.8.32.6)
  
  
  Thus, the 90% Confidence Interval is
  (31.8.32.6)
  .
  
• The 90% Confidence Interval is given by:
  
  S (T-- n * tm-10.05 , T + tn-10.05 ) 12 이녁
  
  where,
  
  7 = 7
  
  
  ΣΕΤ 5.07 ΑΙ Ξ 0.724285714
  
  
  5 = Σ(; – )2 7-1 = 0.39757
  
  
  Now,
  
  t6:0.05 1.94318
  
  
  Putting in the given values, we get,
  
  (0.724285714 0.39757 0.39757 * 1.94318,0.724285714+ * 1.94318) V7
  
  
  = (0.432289233, 1.016282195)
  
  
  (0.432.1.016)
  
  
  Hence, the 90% confidence Interval is
  (0.432.1.016)
  . Since, the upper bound is greater than 1, there appears to be too much mercury in tuna sushi.
  
• The 95% Confidence Interval for pulse rate of females is given by:
  
  。 ( * tm-1:0.025, C+ *th-1;0.025. n n
  
  As visible, the data for females is:

  78
  97
  59
  66
  56
  85
  80
  87
  89
  58
  34
  68
  86
  77
  80
  67
  64
  78
  86
  82
  71
  77
  85
  92
  90
  88
  89
  93
  66
  89
  82
  82
  76
  56
  98
  72

  
  Hence, the observed values are:
  
  n = 36
  
  
  36 Στ 2783 ΑΙ 77.30555556 36 36
  
  
  S = Σ2, (; - Τ)2 36 -1 13.72759358
  
  
  Hence,
  
  t35;0.025 2.03011
  
  
  Putting in the given values, we get,
  
  
  13.72759358 13.72759358 (77.30555556- -*2.03011, 77.30555556+: *2.03011) 36 V36
  
  
  (72.66080139.81.95030972)
  
  
  = (72.7, 82.0
  
  
  Note: As only the confidence interval of blood pressure of females is asked for in the question, I have solved for the females only. However, if the Confidence Interval for blood pressure for males is required, the previous workout will help you out in finding the exact values. However, if you come across any problem, feel free to comment, and I will help you with it.
  
• Given Information:
  
  H = 100
  
  
  0= 13
  
  
  For a sample from Normal population, the 95% Confidence Interval is given by:
  
  (T- * TO.025, T + * T0.025 n n
  
  
  Now, we are to choose n such that,
  
  VI 7 n
  
  
  Now,
  
  T0.025 = 1.960
  
  Hence, putting in the values, we get,
  
  13 * 1.960 s 7 Vn
  
  
  25.48 2 <
  
  
  25.48 Vn>
  
  
  V n 3.64
  
  
  n> 13.2496
  
  
  
  
  Hence, required minimum sample size is 14.
  
  

The first answer is $31.8\;hg<\mu<32.6\;hg$ .
The second answer is $0.432\;ppm<\mu<1.016\;ppm$ .
The third answer is and
the fourth answer is $n=14$ .

I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)