Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels

Question

Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at an archaeological site. At one excavation, a sample of 16 potsherds indicated that 62 were of the three-circle, red-on-white pattern. (a) Find a point estimate p for the proportion of all ceramic potsherds at this site that are of the three-circle, red-on-white pattern. (Round your answer to four decimal places.) (b) Compute a 95% confidence interval for the population proportion p of all ceramic potsherds with this distinctive pattern found at the site. (Round your answers to three decimal places.) lower limit upper limit Submit Answer Save Progress -/1 points BBBasicStat:88. R.010 My Notes Ask Your Teacher + Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 66 students in the highest quartile of the distribution, the mean score was x = 176.10. Assume a population standard deviation of ? 7.59. These students were all classified as high on their need for closure. Assume that the 66 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1.9 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.) students

Explanation / Answer

p= 62/161=0.38509

q= 1-p=0.61491

n= 161

alpha=0.05 then Z(alpha/2)= 1.96

Margin of error E=Z(alpha/2)*sqrt(p*q/n)

=1.96*sqrt(0.3850*0.6149/161)

=0.07516

95% Confidence interval for population proportion =(p-E,p+E)

rounded lower bound= 0.3099

rounded upper bound= 0.4603

0.310 ?P ? 0.460

....................

answers

point estimate =0.3851

rounded lower bound= 0.310

rounded upper bound= 0.460

....................

sigma= 7.59

MOE= 1.9

Zalpha/2= 2.576

we know the relation,

E=Z(alpha/2)*sigma/sqrt(n)

1.9=2.576*7.59/sqrt(n)

n= 105.8931987

n= 106

..............

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