Question

"Unknown cultural affiliations and loss of identity at high elevations." These are words used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not to take trade wares to temporary settings and/or isolated areas. As elevation zones of prehistoric people (in what is now the state of New Mexico) increased, there seemed to be a loss of artifact identification. Consider the following information. Elevation Zone Number of Artifacts Number Unidentified 7000-7500 ft 113 73 5000-5500 ft 145 20 Let p1 be the population proportion of unidentified archaeological artifacts at the elevation zone 7000-7500 feet in the given archaeological area. Let p2 be the population proportion of unidentified archaeological artifacts at the elevation zone 5000-5500 feet in the given archaeological area. (a) Find a 95% confidence interval for p1 − p2. (Round your answers to three decimal places.)

lower limit=

upper limit=

Answer 1

sample #1   ----->              
first sample size,     n1=   113          
number of successes, sample 1 =     x1=   73          
proportion success of sample 1 , p̂1=   x1/n1=   0.6460          
                  
sample #2   ----->              
second sample size,     n2 =    145          
number of successes, sample 2 =     x2 =    20          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.1379          
                  
difference in sample proportions, p̂1 - p̂2 =     0.6460   -   0.1379   =   0.5081

level of significance, α =   0.05              
Z critical value =   Z α/2 =    1.960   [excel function: =normsinv(α/2)      
                  
Std error , SE =    SQRT(p̂1 * (1 - p̂1)/n1 + p̂2 * (1-p̂2)/n2) =     0.0533          
margin of error , E = Z*SE =    1.960   *   0.0533   =   0.1045
                  
confidence interval is                   
lower limit = (p̂1 - p̂2) - E =    0.508   -   0.1045   =   0.404
upper limit = (p̂1 - p̂2) + E =    0.508   +   0.1045   =   0.613