Math153 J. Dykacz

4/30/01  Extra Review Problems Test 3 (BLUE)

 

1.      Assume that the mean hourly wage in a traditionally female occupation is $10 per hour ( m =10).  Men have entered the occupation, and we want to test how the mean hourly wage for males compares with the $10.  A random sample of 36 males is taken; the sample mean is $10.90 and the sample standard deviation is $3.

a)      At the 5% significance level, is the mean hourly wage for males $10 or is it different from $10?

H0: ________________________

Ha: ________________________

 

1.        a = _______

2.  Test statistic: ________________     p-value: ____________________

3.  Conclusion: ____________________________________________

 

 

b)      At the 5% significance level, is the mean hourly wage for males greater than $10?

H0: ________________________

Ha: ________________________

 

1.  a = _______

2.  Test statistic: ________________     p-value: ____________________

3.  Conclusion: ____________________________________________

 

 

c)      At the 1% significance level, is the mean hourly wage for males greater than $10?

 

H0: ________________________

Ha: ________________________

 

1.  a = _______

2.  Test statistic: ________________     p-value: ____________________

3.  Conclusion: ____________________________________________

 

 

2.      A researcher wants to estimate the average number of cigarettes smoked per day by teenage boys who are smokers.  Assume a 99% confidence interval will be calculated with a margin of error of not more than 0.5 (1/2 a cigarette).  Assume that the standard deviation is 2.7.  Find the appropriate sample size.

 

 

 

3.      A poll is to be conducted among a sample of students at a college to determine if they are satisfied (or not) with extracurricular activities.  A 90% confidence interval is to be formed of the percent of students who are satisfied with extracurricular activities; the margin of error should be no more than 5%..

a)      From a previous study, the percent was 63%.  Find the appropriate sample size.

 

 

b)  Assume that no previous, related study was done.  Find the appropriate sample size.

 

Answers

1a) H0 : m  =10

      Ha :  m 10

     1. a=.05

     2. t =1.80,  p-value=.0805

     3.  Do not reject H0

     

 

1b) H0 : m  10

      Ha :  m >10

     1. a=.05

     2. t = 1.80,   p-value=.0402

     3.  Reject H0

 

1c) H0 : m  10

      Ha :  m >10

     1. a=.01

     2. t = 1.80, p-value=.0402

     3.  Do not reject H0

 

2  n = = = 193.349025 = 194

 

3.  a) n =  = = 252.309771 = 253

 

     b) n =  = = 270.6025 = 271