Question

pt 8 of 23 (18 complete) HW Sc 7.4.55 A random sample of size n 80 yielded p 0.75 a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p? Explain. b. Construct a 99% confidence interval for p. c. Interpret the 99% confidence interval. d. Explain what is meant by the phrase "99% confidence interval. a. Is the sample large enough? OA. No, because npz 15 and nq< 15. O B. Yes, because np2 15 and nq 2 15 Click to select your answer and then click Check Answer. 3 parts remaining Clear All PREVIOUS

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Answer 1

a)

np^ = 60

nq^ =20

yes, because np^ ≥10 and nq^≥10

b)

Level of Significance,   α =    0.01          
Number of Items of Interest,   x =   60          
Sample Size,   n =    80          
                  
Sample Proportion ,    p̂ = x/n =    0.750          
z -value =   Zα/2 =    2.576   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0484          
margin of error , E = Z*SE =    2.576   *   0.0484   =   0.1247
                  
99%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.750   -   0.1247   =   0.6253
Interval Upper Limit = p̂ + E =   0.750   +   0.1247   =   0.8747
                  
99%   confidence interval is (   0.625   < p <    0.875   )

c)

we are 99% confident that true population proportion will lie within the confidence interval

d)

If we took repeated samples, approximately 99% of the confidence intervals calculated from those samples would contain the true value of the population proportion.