Based on information from harper’s index, 37% of adult americans believe in extraterrestrials. out of a random sample of 100 adults who attended college, 47 claim they believe in extraterrestrials. does this indicate that the proportion of individuals who attended college and believe in extraterrestrials is higher than the proportion found by harper’s index? use α = 0.05 for your confidence interval, show all steps, clearly explain your conclusion

z(s)  is in the rejection zone , therefore we reject H₀

We have enough evidence to claim the proportion of individuals who attended college and believe in extraterrestrials is bigger than 37%

Step-by-step explanation:

We have a prortion test.

P₀  =  37 %         P₀  = 0,37

sample size  =  n  =  100

P sample proportion   =   P  = 47 %        P  =  0,47

confidence interval  95 %

α  =   0,05  

One tail-test  (right tail) our case is to show if sample give enough information to determine if proportion of individual who attended college is higher than the proportion found by Harper´s index.

1.-Hypothesis:

H₀      null hypothesis                        P₀  =  0,37

Hₐ  alternative hypothesis                P₀  >  0,37

2.-Confidence interval 95 %

α  =   0,05        and    z(c)  =  1.64

3.-Compute of z(s)

z(s)  =  [  P  -  P₀  ]  /√(P₀Q₀/n) ]  

z(s)  =  [ (  0,47  -  0,37  ) /  √0.37*0,63/100

z(s)  = 0,1 /√0,2331/100     ⇒   z(s)  = 0,1 /0,048

z(s)  = 2.08

4.-Compare  z(s)   and  z(c)

z(s) > z(c)        2.08  > 1.64

5.-Decision:

z(s)  is in the rejection zone , therefore we reject H₀

We have enough evidence to claim the proportion of individuals who attended college and believe in extraterrestrials is bigger than 37%

step-by-step explanation:

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step-by-step explanation: