Question

Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication. Similarities and Differences in a Random Sample of 375 Married Couples Number of Similar Preferences Number of Married Couples All four 27 Three 124 Two 118 One 70 None 36 Suppose that a married couple is selected at random.

1(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.) 0=____ 1=____   2=_____ 3=_____ 4=________

1(b) Do the probabilities add up to 1? Why should they?

a. Yes, because they do not cover the entire sample space.

b. No, because they do not cover the entire sample space.

c. Yes, because they cover the entire sample space.

d. No, because they cover the entire sample space.

What is the sample space in this problem?

a. 0, 1, 2, 3 personality preferences in common

b. 1, 2, 3, 4 personality preferences in common

c. 0, 1, 2, 3, 4, 5 personality preferences in common

d. 0, 1, 2, 3, 4 personality preferences in common

2. Consider the data set.

• 2, 3, 4, 5, 6

(a)

Find the range. (Enter an exact number.)=______

(b)

Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)=______

(c)

Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)=____

Answer 1

1)

a. Individually we have been different number of similarities between the couples. Since these similarities vary, X - number of similarities' is a variable. Given the number of couples with their number of similarities we arrange the data in a frequency table. To find the probability we can find the relative freq

Relative freq = freq / Total freq

Eg for four similarities

X = 4 F = 27

Relative freq = 27 / 375

X	Freq	P(X)
0	36	0.096
1	70	0.1867
2	118	0.3147
3	124	0.3307
4	27	0.072
Total	375	1

b.

Do the probabilities add up to 1? Why should they?

c. Yes, because they cover the entire sample space.

sample space includes all the 'x' and their corresponding freq.

c. What is the sample space in this problem?

d. 0, 1, 2, 3, 4 personality preferences in commonc.

Since 'X' can take 0 - 4

2.)

	X
1	2
2	3
3	4
4	5
5	6
Total	20

(a)

Find the range.

Range = Max - min

= 6 - 2

Range= 4

	X	X^2
1	2	4
2	3	9
3	4	16
4	5	25
5	6	36
Total	20	90
Sample SD	1.5811
Population SD	1.4142

(b)

For a sample deviation we do not have the entire population data but a part of it.

SD =

SD sample Sx = 1.5811

(c)

For the population SD we use 'n' instead of 'n-1'

Pop SD =

σ = 1.4142