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The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. From the 505 sampled US residents with a college degree, the average number of hours worked each week was 41.8 hours with a standard deviation of 15.1 hours. For those 667 residents without a degree, the mean was 39.4 hours with a standard deviation of 15.1 hours.

Required:
Conduct a hypothesis test at significance level 0.05.

Respuesta :

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Answer:

We reject H0 ; We conclude that mean number of resident with a college degree is greater than those without degree.

Step-by-step explanation:

H0 : μ1 = μ2

H1 : μ1 > μ2

n1 = 505

s1 = 41.8

x1 = 15.1

n2 = 667

s2 = 39.4

x2 = 15.1

df = smaller, n - 1 ; 505 - 1= 504

Test statistic :

(x1 - x2) / √((s1²/n1) + (s2²/n2))

(41.8 - 39.4) /√((15.1^2 / 505) + (15.1^2 / 667))

2.4 / 0.8907014

Test statistic = 2.6945057

Using the Pvalue calculator from test statistic :

df = 504 ; α = 0.05

Pvalue = 0.0036

Decision region : If Pvalue < α ; Reject H0

0.0036 < 0.05 ; We reject H0 ; We conclude that mean number of resident with a college degree is greater than those without degree.