Question

1)For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 65 professional actors, it was found that 40 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit =
upper limit =

2)For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 502 judges, it was found that 295 were introverts.

(a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answers to two decimal places.)

lower limit =
upper limit =

3)Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.

Weights (in lb) of pro football players: x₁; n₁ = 21

244	263	255	251	244	276	240	265	257	252	282
256	250	264	270	275	245	275	253	265	270

Weights (in lb) of pro basketball players: x₂; n₂ = 19

205	200	220	210	192	215	222	216	228	207
225	208	195	191	207	196	181	193	201

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to one decimal place.)

x1 =
s1 =
x2 =
s2 =

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to one decimal place.)

lower limit =
upper limit =

Answer 1

1)

a)

Number of Items of Interest,   x =   40
Sample Size,   n =    65
      
Sample Proportion ,    p̂ = x/n =    0.6154

b)

z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.060343          
margin of error , E = Z*SE =    1.960   *   0.06034   =   0.1183
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.61538   -   0.11827   =   0.497
Interval Upper Limit = p̂ + E =   0.61538   +   0.11827   =   0.734
                  
95%   confidence interval is (   0.50 < p <    0.73 )
===============

2)

a)

Number of Items of Interest,   x =   295
Sample Size,   n =    502
      
Sample Proportion ,    p̂ = x/n =    0.5876
      

b)

z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.021971          
margin of error , E = Z*SE =    1.960   *   0.02197   =   0.0566
                  
99%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.58765   -   0.05659   =   0.531
Interval Upper Limit = p̂ + E =   0.58765   +   0.05659   =   0.644
                  
99%   confidence interval is (   0.53 < p <    0.64 )