The estimated proportions of undergraduates owning a phone is 43% in 2010 and 89

Question

The estimated proportions of undergraduates owning a phone is 43% in 2010 and 89% in 2014. Given that the sample size of each SRS is 1200 students, we want to test whether the proportion of undergraduate cell phone owners has more than doubled in the last 4 years.

a) Compute the quantity p1-2p2 where p1 is the 2014 estimate and p2 is the 2010 estimate.

b) Using the rules for variances, compute the standard error of this estimate.

c) Compute the z statistic, P-value and carry a hypothesis test at the 5% significance level.

Explanation / Answer

a) Compute the quantity p1-2p2 where p1 is the 2014 estimate and p2 is the 2010 estimate.

0.89-0.43 =0.46

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b) Using the rules for variances, compute the standard error of this estimate.

variance= (p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.89*(1-0.89)/1200+0.43*(1-0.43)/1200)

=0.0002858333

standard error= sqrt(0.0002858333)

=0.01690661

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c) Compute the z statistic, P-value and carry a hypothesis test at the 5% significance level.

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=0.46/0.01690661

=27.21

It is a right-tailed test.

So the p-value = P(Z>27.21) =0 (from standard normal table)

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can conclude that the proportion of undergraduate cell phone owners has more than doubled in the last 4 years.

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