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In a random sample of 850 high school students in large metropolitan areas, 768 said they had access to the internet during school hours. In an independent random sample of 355 high school students in rural communities, 308 said they had access to the internet during school hours. What is the p-value for a significance test to determine if these data provide evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours?

Sagot :

akiran007

Answer:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

Step-by-step explanation:

Let p1= proportion of the high school students having internet access

p2= proportion of the rural school students having internet access

1) The null and alternate hypothesis are

H0: p1≠ p2  against the claim   Ha: p1= p2

2) We choose significance level ∝ =0.05

3) The test statistic under H0 is

z= p1^- p2^/√ p^q^( 1/n1 + 1/n2)

Now

p1^= 768/850= 0.9035

p2^= 308/355= 0.8670

p^= 768+ 308/850+ 355= 1076/1205

p^= 0.8929

q^= 1-p^= 0.1070

Putting the values

z= p1^- p2^/ √p^q^( 1/n1 + 1/n2)

Z= 0.9035-0.8670/sqrt [0.8929*0.1070( 1/850 + 1/355)]

z= 0.0365/ sqrt [ 0.0955403 (0.001176 + 0.002816)]

z= 0.0365/ 0.019531

z= 1.8688

The critical region is  z∝/2 = ± 1.96

The value of z is 1.8666. The value of p is 0.06148 which is greater than 0.05

Conclusion:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

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