A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Hours Of Sleep 39 or Younger 40 or Older
Fewer than 6 38 36
6 to 6.9 60 57
7 to 7.9 77 75
8 or More 65 92

Required:
a. Conduct a test of independence to determine whether hours of sleep are independent of age. Using α= 0.05 level of significance
b. Compute the value of the 2 test statistic.
c. The p-value is:
d. What is your conclusion?

Kindly check explanation

Step-by-step explanation:

Given the data :

Hours of sleep

Age ___<6__6-6.9___ 7-7.9 __≥8 ___total

≤ 39___38___607765240

≥ 40___36___577592260

A.) test of independence for row and column variables :

Null: row and column variables are independent

Alternative : row and column variables are not independent

Expected frequencies :

[(row total) * (column total] / sample size

E1: ((38+60+77+65)*(38+36))/500 = 35.52

E2: ((38+60+77+65)*(60+57))/500 = 56.16

E3: ((38+60+77+65)*(77+75))/500 = 72.96

E4: ((38+60+77+65)*(65+92))/500 = 75.36

E5: ((36+57+75+92)*(38+36))/500 = 38.48

E6: ((36+57+75+92)*(60+57))/500 = 60.84

E7: ((36+57+75+92)*(77+75))/500 = 79.04

E8: ((36+57+75+92)*(65+92))/500 = 81.64

Then performing the Chisquare independence test X²

X² = Σ[(f1-e1)²/e1 + (f2-e2)²/e2... (fn - en)²/en]

F1 to f8 = 38,60,77,65,36,57,75,92

X² = ((38-49.92)^2)/35.52 + ((60-56.16)^2)/56.16 + ((77-72.96)^2)/72.96 + ((65-75.36)^2)/75.36 + ((36-38.48)^2)/38.48 + ((57-60.84)^2)/60.84 + ((75-79.04)^2)/79.04 + ((92-81.64)^2)/81.64

= 4.0070162

X² = 4.00

α = 0.05

Reject Null if p < α

df = (row - 1)*( column - 1)

df = (2 - 1)*(4-1) = 1*3 = 3

To obtain the p value, we can use an online calculator to compute the P-value from the X² square score at α = 0.05 and 3 degree of freedom

p = 0.261

Since ; p > α ; 0.261 > 0.05 ; The result is not significant at α 0.05 ; Hence we fail to reject the Null.

false

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answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)