Question

In: Statistics and Probability

A random sample of sixty (60) long distance truck drivers were each asked if they often...

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 tcrit or Zcrit).

(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 tcalc or Zcalc)

(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 .

Solutions

Expert Solution

a. The sample proportion of long distance truck drivers who often feel tired while driving is given by

b. Here we have to test the hypothesis that the proportion of long distance truck drivers p, who often feel tired while driving has reduced below 70% after the introduction of the new laws. that is weather p <0.7 .To test this the hypotheis is given by

Here Ha represents the alternative hypothesis. So your ans is less than type.

c. To test the hypotheis in part b we need the following test statitics

Our test is one sided and thus by standard normal table, at 10% level of significance the critical value is

 -1.28.

d. Since six months after introducing the new laws, among random sample of 60 long distance truck drivers 34 are feeling tired while driving. so p=34/60= 0.57, so test statistics

e. By comparing the z calculated by its critical value (z cal < z crit), we can say that the null hypotheis can not be accepted.

f.


Related Solutions

A random sample of sixty (60) long distance truck drivers were each asked if they often...
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...
. A researcher selects a random sample of 10 persons from a population of truck drivers...
. A researcher selects a random sample of 10 persons from a population of truck drivers and gives them a driver’s aptitude test. Their scores are 22,3,14,8,11,5,18,13,12, and 12.      (a) Find the estimated standard error of the mean.      (b) Find the 95% confidence interval for the population mean.
A random sample of 13 students were asked how long it took them to complete a...
A random sample of 13 students were asked how long it took them to complete a certain exam. The mean length of time was 105.6 minutes, with a standard deviation of 71.7 minutes. Find the lower bound of the 90% confidence interval for the true mean length of time it would take for all students to complete the exam. Round to one decimal place (for example: 108.1)
10) A random sample of 13 students were asked how long it took them to complete...
10) A random sample of 13 students were asked how long it took them to complete a certain exam. The mean length of time was 120.1 minutes, with a standard deviation of 84.0 minutes. Find the lower bound of the 90% confidence interval for the true mean length of time it would take for all students to complete the exam. Round to one decimal place (for example: 108.1). Write only a number as your answer. Do not write any units....
2. A random sample of 395 people were surveyed and each person was asked to report...
2. A random sample of 395 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table:     High School   Bachelors   Masters   Ph.d.   Total Female   60   54   46   41   201 Male   40   44   53   57   194 Total   100   98   99   98   395 a. Are gender and education level dependent at 5% level of significance? (6mks) b.State and explain two methods of studying...
A random sample of 100 adults were surveyed, and they were asked if the regularly watch...
A random sample of 100 adults were surveyed, and they were asked if the regularly watch NFL games.  They were asked in their favorite team had ever won the Super Bowl. Won Super Bowl Did not win Super Bowl Row total Watch games 24 56 80 Do not watch games 11 9 20 Column total 35 65 100 Find: a) P(watch NFL games given their favorite team won the Super Bowl) b) P(favorite team won the Super Bowl and watch NFL...
A simple random sample was conducted of 1405 Canadian adults. They were asked whether they were...
A simple random sample was conducted of 1405 Canadian adults. They were asked whether they were in favor of tighter enforcement of tobacco laws. Of the 1405 adults, 1060 responded yes. Obtain a 95% confidence interval for the proportion of Canadian adults who are in favor of tighter enforcement of tobacco laws. Of 15, 344 Virginians tested for COVID-19 in March of 2020, 1,484 had positive or presumptive positive results for the virus. Assuming the other 49 states had results...
A random sample of 20 workers in a factory were asked to report the age of...
A random sample of 20 workers in a factory were asked to report the age of their car and how many miles the vehicle had on it. A computer printout resulted in the following information. Variable Coef SE Coef t-ratio Prob Constant 7288.54 6591 1.11 <0.2826 Age 11630.6 1249 9.31 <0.0001 R sq = 82% R sq adj = 81.1% s = 19280 Find the LSRL A new worker starts next week and we know that his car is 7...
A random sample of sociology majors at the University of Methods were asked a series of...
A random sample of sociology majors at the University of Methods were asked a series of questions about their major advisor. Interpret their answers to the following question: "My advisor encourages me to see him/her." Level of Agreement frequency: Strongly agree - 19 Agree - 29 Undecided - 34 Disagree - 13 Strongly disagree - 14 No answer - 44
A pediatrician asked a random sample of parents to report how long it took their toddler...
A pediatrician asked a random sample of parents to report how long it took their toddler to fall asleep at night. Among 51 toddlers the mean time to fall asleep at night was 23.4 minutes with a standard deviation of 6.7 minutes. Fill in the missing values (rounded to one digit after the decimal point) to estimate the parameter. Using 95% confidence, the mean time to fall asleep among all toddlers is between ______ and ______.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT