Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p 0.08; z = 4.66; P-value 0.08; z = -4.66; P-value 0.00001.This data shows conclusive evidence that the proportion in car commuting is greater than 8%. C) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.08; z = 4.66; P-value

Question

Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.08; z = 4.66; P-value < 0.00001.This data shows conclusive evidence that the proportion in car commuting is greater than 8%. B) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.08; z = -4.66; P-value > 0.00001.This data shows conclusive evidence that the proportion in car commuting is greater than 8%. C) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.08; z = 4.66; P-value < 0.99999.This data shows no evidence that the proportion in car commuting is greater than 8%. D) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.08; z = 4.66; P-value < 0.99999.This data shows no evidence that the proportion in car commuting is greater than 8%. E) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.08; z = -4.66; P-value > 0.99999.This data shows no evidence that the proportion in car commuting is greater than 8%.

Quizplus · Accepted Answer

The appropriate hypothesis to test is:
Null hypothesis: p = 0.08 (proportion of employees who commute by car is the same as 5 years ago)
Alternative hypothesis: p > 0.08 (proportion of employees who commute by car is greater than 5 years ago)

The conditions for using a z-test are satisfied:
1) Random sample: The employees are selected randomly.
2) Independence: The employees commute to work independently.
3) Sample size: The sample size is sufficiently large since np and n(1-p) are both greater than 10.

The test statistic is z = (p̂ - p) / √(p(1-p) / n) = (0.12 - 0.08) / √(0.08(1-0.08) / 1000) = 4.66.

The P-value is less than 0.00001, which means that the probability of observing a sample proportion of 0.12 or more if the true proportion is 0.08 is extremely small. Therefore, we reject the null hypothesis and conclude that there is conclusive evidence that the proportion of employees who commute by car is greater than it was five years ago.

Five Years Ago,a Company Found That 8% of Its Employees H0\mathrm { H } _ { 0 }H0​

Five Years Ago,a Company Found That 8% of Its Employees $\mathrm { H } _ { 0 }$