Question

A random sample of sixty (60) long distance truck drivers were each asked if they often feel tired while driving. Forty five (45) of the truck drivers replied “yes”.

(a) What is the sample proportion of long distance truck drivers who often feel tired while driving (two decimal places)? Type only the numeric answer in the box .

The government introduced new laws requiring long distance truck drivers to take minimum rest breaks. Prior to introducing the new laws, the true proportion of long distance truck drivers who often felt tired while driving was 70%. Six months after introducing the new laws, another random sample of 60 long distance truck drivers is surveyed with 34 indicating they often feel tired while driving.

(b) State the direction of the alternative hypothesis to test whether the proportion of long distance truck drivers who often feel tired while driving has reduced below 70% after the introduction of the new laws. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box .

(c) State the critical value to conduct the test at 10% level of significance (two decimal places). Type only the numeric value with the correct sign in the box . (No need to specify whether it is t_crit or Z_crit).

(d) What is the calculated test statistic (two decimal places)? Type only the numeric value with   the correct sign in the box . (No need to specify whether it is t_calc or Z_calc)

(e) Is the null hypothesis rejected for this test? Type yes or no in the box .

(f) What is the p-value for this test (four decimal places)? .

(g) If it was later found that the true population proportion of long distance truck drivers who indicated they often felt tired while driving after introduction of the new laws was 72%, determine the nature of the decision made in the test in part (e). Type cd (correct decision), 1 (a Type I error was made) or 2 (a Type II error was made) as appropriate in the box .

Answer 1

(a) Sample proportion of long distance drivers who often feel tired while driving is given by

45 / 60 = 0.75

Answer : 0.75

b) The null hypothesis is

H0 : p0.70

As we are to test whether p is less than 0.70 ,the alternative hypothesis is

H1: p < 0.70

( the test is one tailed;  left tailed)

Direction of Alternative hypothesis is lt( less than )

Answer : lt

c) For , the left tailed critical value of z is

Z_crit = -1.29

Answer : 1.29

d) Test statistic

where

Therefore ,

Answer : -2.25

e) Since I z I > I Z_crit I

We reject the null hypothesis

Answer : YES

f) P value = P( Z < -2.25) = 0.0122 ( from z table, left tailed)

Answer : 0.0122

g) As , on the basis of the test we reject H0 and conclude that p < 0.70

As the true proportion is p=0.72 , that is null hypothesis is true

That means we have rejected the true null hypothesis

Our decision is not correct

Type I error is the error of rejecting a true null hypothesis

Answer : 1 ( type I error was made)