A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, $z = \frac { \hat { p } - \mathrm { p } _ { 0 } } { \sqrt { { p } _ { 0 } \left( 1 - \mathrm { p } _ { 0 } \right) / \mathrm { n } } }$
-A research group wants to determine whether the proportion of car accidents caused by drivers using cell phones has changed from the previous value of 13%. They obtained 10,000 auto accident
Reports and found that 14% were caused by drivers using cell phones. The hypotheses are $\mathrm { H } _ { 0 } : \mathrm { p } = 0.13 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.13$
where p is the proportion of car accidents caused by drivers using cell
Phones.

Question

A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, $z = \frac { \hat { p } - \mathrm { p } _ { 0 } } { \sqrt {  { p } _ { 0 } \left( 1 - \mathrm { p } _ { 0 } \right) / \mathrm { n } } }$
-A research group wants to determine whether the proportion of car accidents caused by drivers using cell phones has changed from the previous value of 13%. They obtained 10,000 auto accident
Reports and found that 14% were caused by drivers using cell phones. The hypotheses are $\mathrm { H } _ { 0 } : \mathrm { p } = 0.13 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.13$ 
where p is the proportion of car accidents caused by drivers using cell
Phones.

Quizplus · Accepted Answer

The test statistic $z$ is calculated using the formula given, with $\hat { p } = 0.14$, $p_0 = 0.13$, and $n = 10000$. Substituting these values into the formula gives $z = \frac { 0.14 - 0.13 } { \sqrt { 0.13 \times (1 - 0.13) / 10000 } } = \frac { 0.01 } { \sqrt { 0.13 \times 0.87 / 10000 } } = \frac { 0.01 } { \sqrt { 0.1131 / 10000 } } = \frac { 0.01 } { \sqrt { 0.00001131 } } = \frac { 0.01 } { 0.003364 } \approx 2.974$.

A Hypothesis Test Is to Be Performed for a Population z=p^−p0p0(1−p0)/nz = \frac { \hat { p } - \mathrm { p } _ { 0 } } { \sqrt { { p } _ { 0 } \left( 1 - \mathrm { p } _ { 0 } \right) / \mathrm { n } } }z=p0​(1−p0​)/n​p^​−p0​​

A Hypothesis Test Is to Be Performed for a Population $z = \frac { \hat { p } - \mathrm { p } _ { 0 } } { \sqrt { { p } _ { 0 } \left( 1 - \mathrm { p } _ { 0 } \right) / \mathrm { n } } }$