Question

X̄ = 190.4 cm

      s = 13.8 cm

      n = 73 (Unitless)

      Confidence = 98 %

      IT IS IMPORTANT TO REPORT CONFIDENCE INTERVALS CORRECTLY:

      Report them as "(L < μ < U) with __ % Confidence",

       with appropriate numbers substituted for L, U and Confidence.

      Omit L or U if the Confidence Interval does not have a Lower or Upper Limit.

Question(s)

1. If you repeated this problem many times--with a new sample collected from X each time--what percentage of the Confidence Intervals thus estimated would you expect to include the true mean?

2. What is the Significance of the Confidence Interval? Note: answer is decimal, NOT percent.

3. What probability will be used to calculate the Critical Value (i.e., is placed in tail)?Again: answer is decimal, NOT percent.

4. Calculate the Degrees of Freedom.

5. Calculate the Critical Value used to determine the Confidence Limit(s). Use a calculator, Excel, or other software.

6. Calculate the Lower Limit of the Confidence Interval.

7. Calculate the Upper Limit of the Confidence Interval.

Answer 1

1. Since the confidence level is 98%, it means that if we repeat this problem many times with a new sample collected from X each time, 98% of the time we would expect the confidence Interval to contain the true mean.

2. Significance of the confidence Interval= 1-98% = 0.02

3. Probability that will be used = 0.02/2 = 0.01

4. Df = n-1= 72

5. Critical value, t 0.01,72 = 2.38 (from the t-distribution tables)

6. Now, Lower limit = 190.4 -2.38*13.8/√73 = 186.56

7. Upper limit = 190.4 + 2.38*13.8/√73 = 194.24