Question

computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 states, from USStates dataset, is given in the table below. since all 50 states are included this is population not a sample

variable N N    mean. se mean. stdev. minimum
                50, 0, 28.766, 0.476,    3.369, 21.300
Q1.          median. Q3.      Maximum
26.375, 29.400, 31.150, 35.100

a. what are the mean and standard deviation
u=
o=

b. calculate the z- score for the largest value and interpret in terms standard deviation
z-score=
the maximum 35.1% obese is
z-score =
the minimum of 21.3% is

c. the distribution is relatively symmetric and bell shaped. give interval that is likely to contain about 95%
the interval is.        % to.         %

Answer 1

Answer : Computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 US states, from the USStates dataset, is given in table below. Since all 50 US states are included, this is a population, not a sample.

Variable

N N*             Mean    SE Mean   StDev     Minimum    Q1   Median     Q3       Maximum                           50 0                28.766 0.476     3.369       21.300        26.375   29.400 31.150 35.100

Solution :

a) the mean and standard deviation :

     Mean, mu= 28.766%

      Standard deviation, σ = 3.369%

b) the z-score for the largest value and interpret it in terms of standard deviations. :

    z- score = x - mean/ std. deviation

                   = (35.100 - 28.766 )/3.369

                  = 1.880

The maximum 35.1 % obese is 1.880 and std.deviation above the mean.

The z-score for smallest value:

z-score = x - mean/ std.deviation

                = (21.300 - 28.766)/ 3.369

                 =-2.216

The minimum of 21.300% obese is 2.216 and standard deviations below the mean.

The 95% interval is = ( mean-2*sd, mean+2*sd)

                                  =(28.766 - 2* 3.369, 28.766 + 2*3.369)

                                  = (22.028, 35.504)

Therefore, the interval is 22.028% to 35.504%.