Question

Question
A police officer claims that the proportion of drivers wearing a seat belt in a certain area is less than 40%.
To test this claim, the officer collects a random sample of 80 drivers and monitors if the driver was wearing a seat belt.
From this sample of 80 drivers, the police offers observes that 34 were wearing seat belts.
Assume the conditions needed to conduct a one sample proportion test are satisfied.
The setup for the null and alternative hypothesis is as follows:
H : p = 0.40; H, :p < 0.40, which is a left-tailed test.
Compute the test statistic and p-value for this Hypothesis test using Excel and round your answers to 3 decimal places.

Answer 1

Answer:

0.456

0.324

Explanation:

The null and alternative hypothesis :

H0 : p = 0.40; HA :p < 0.40

Test statistic :

(Ph - P) / sqrt[(p*(1-p))/n]

Ph = X / n

X = 34 ; n = sample size = 80

Ph = 34 / 80 = 0.425

(0.425 - 0.4) / sqrt[(0.4(0.6)) / 80]

0.025 / sqrt(0.003)

0.025 / 0.0547722

Test statistic = 0.4564359

Test statistic = 0.456

Using the P-value from Zscore calculator :

Significance level of 95% ; one tailed

Z statistic value = 0.456

P value = 0.324195

= 0.324 ( 3 decimal places)

Answer 2

Answer:

test statistic=0.456  p value=0.676

Explanation: