Question

(Heights of Presidents since 1900) Listed below are the heights (in inches) of the Presidents who started serving in 20th until today. Assume that these values are sample data from some larger population.

67, 70, 72, 71, 72, 70, 71, 74, 69, 70.5, 72,

75, 71.5,   69.5, 73, 74, 74.5, 71.5, 73.5, 72.5,

(a) Find the mean

(b) Find the median

(c) Find Q₁ and Q₃

(d) Construct a boxplot for the data

(e) Find the range

(f) Find the standard deviation and variance

(g) Assume that the values are sample data, construct a 99% confidence interval to estimate of the population mean

(h) Assume that the values are sample data, construct a 99% confidence interval fro the population standard deviation

(i) The mean height of men is 69.0 inches. Use a 0.05 significance level to test the claim that this sample comes from a population with a mean greater than 69.0 inches. Do Presidents appear to be taller than a typical man in U. S.? (Show hypothesis test details, test statistic, decision making, and conclusion)

Answer 1

Based on given sample information we have,

The sample size is n = 20n=20. The provided sample data along with the data required to compute the sample mean \bar XXˉ and sample variance s^2s2 are shown in the table below:

	X	X2
	67	4489
	70	4900
	72	5184
	71	5041
	72	5184
	70	4900
	71	5041
	74	5476
	69	4761
	70.5	4970.25
	72	5184
	75	5625
	71.5	5112.25
	69.5	4830.25
	73	5329
	74	5476
	74.5	5550.25
	71.5	5112.25
	73.5	5402.25
	72.5	5256.25
Sum =	1433.5	102823.75

  

a) & f) The mean is Xbar = 71.675

And sample Standerd deviation s = 2.021 and sample Variance s^2= 4.086.

b) , c), d) & e) is calculated using following steps,

The first task is to compute the median and the quartiles. And, in order to compute the median and the quartiles, the data needs to be put into ascending order, as shown in the table below

Position	X (Asc. Order)
1	67
2	69
3	69.5
4	70
5	70
6	70.5
7	71
8	71
9	71.5
10	71.5
11	72
12	72
13	72
14	72.5
15	73
16	73.5
17	74
18	74
19	74.5
20	75

b) The median is 71.75 inches.

c) The Q1 is 65.25 & Q3 is 78.25.

d) the boxplot is given above.

e) The range is 8.

Range = Max - Min

Ramge = 75 - 67 = 8  

The 99% confidence interval for population mean is computed using t distribution because here the population standard deviations is unknown and the Confidence Interval for population standard deviations is computed using chi square distribution.

f) & g) is calculated using following steps,

i) The Hypothesis test that the claim is the president height is more than 69 inches is test using t test at 0.01 level of significance ( assumed) as below,

The t critical value is calculated using t table or using Excel.

Hope you understood then please RATE POSITIVE ?.

Thank you.