Question

1. According to the Pew Research Center, 73% of adults in the U.S. have broadband access in their homes. An internet access advocacy group thinks that rate is different among Saint Paul high school students.

A. What are the null and alternative hypotheses for a test on this claim? Is this a one-sided or two-sided test? Is the claim represented by the null or alternative hypothesis?

b. A survey of Saint Paul high school students finds that 135 out of 197 students have broadband access in their home. Conduct a test at α = 0.05 level of confidence of the claim that Saint Paul high school students have access to broadband at a different rate than U.S. adults. Be sure to state your conclusion in the context of the question.

Answer 1

a)

The null and alternative hypothesis are

H0: p = 0.73

Ha: p 0.73 (Claim)

This is two tailed test.

b)

Sample proportion = 135 / 197 = 0.6853

Test statistics

z = - p / sqrt( p ( 1 - p) / n)

= 0.6853 - 0.73 / sqrt( 0.73 * 0.27 / 197)

= -1.10

This is test statistics value.

p-value = 2 * P( Z < z)

= 2 * P (Z < -1.10)

= 2 * 0.1357

= 0.2714

Since p-value > 0.05 level, we does not have sufficient evidence to reject H0.

We conclude at 0.025 level that we fail to support the claim.