Question

Select the most appropriate response. Five years ago, a survey found that the proportion of city employees who commute to work by car is 8%. A local city commissioner claims that the percentage is higher than it was five years ago. Data on employee commuting by car was collected on a random sample of 1000 employees and found 12% of employees commute by car. Test an appropriate hypothesis and state your conclusion at the 10% level of significance. State the alternative hypothesis, the test statistic, your decision and your findings. Note: The p-value is 0.00000156.

a) HA: p = 0.08; z = 4.66; Do not reject the null hypothesis. This data does not show a proportion in car commuting greater than 8%.

b) HA: p > 0.08; z = 4.66; Reject the null hypothesis. This data shows a proportion in car commuting greater than 8%.

c) HA: p < 0.08; z = -4.66; Reject the null hypothesis. This data does not show a proportion in car commuting greater than 8%.

d) HA: p > 0.08; z = -4.66; Do not reject the null hypothesis. This data shows a proportion in car commuting greater than 8%. e) HA: p < 0.08; z = 4.66; Reject the null hypothesis. This data does not show a proportion in car commuting greater than 8%

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.08

Ha : p > 0.08

= 0.12

n = 1000

P0 = 0.08

1 - P0 = 1 -0.08 = 0.92

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.12 -0.08/ [0.08*(0.92) /1000 ]

= 4.66

P(z > 4.66) = 1 - P(z < 4.66 ) = 0

P-value = 0.0000

= 0.10  

0 < 0.10

b) HA: p > 0.08; z = 4.66; Reject the null hypothesis. This data shows a proportion in car commuting greater than 8%.