Chapter 8, Review Exercises, Problem 102 Your answer is partially correct. Try a

Question

Chapter 8, Review Exercises, Problem 102 Your answer is partially correct. Try again Internet prices for glasses are often considerably lower than those at the brick and mortar stores but quality is another question. To address that issue, some optometrists ordered 154 adult pairs of spectacles from various online stores. 6 Of the 154 pairs of spectacles, 44 pairs of eye wear contained at least one lens that did not pass optical analysis testing. (a) Conduct a test of hypotheses with the intent of establishing that that the probablity of not passing the optical analysis testing is greater than 0.20. Use level of significance 0.025 2.659 We reject j Ho at = 0.025 Round your answer to three decimal places. (b) Calculate the -value and comment. 0039 rejected the null hypothesis. The p-value is Round your answer to four decimal places. Click if you would like to Show Work for this question: Open Show Work SO, we would have

Explanation / Answer

Given that,

possibile chances (x)=44

sample size(n)=154

success rate ( p )= x/n = 0.2857

success probability,( po )=0.2

failure probability,( qo) = 0.8

null, Ho:p=0 .2  

alternate, H1: p>0.2

level of significance, = 0.025

from standard normal table,right tailed z /2 =1.96

since our test is right-tailed

reject Ho, if zo > 1.96

we use test statistic z proportion = p-po/sqrt(poqo/n)

zo=0.28571-0.2/(sqrt(0.16)/154)

zo =2.6592

| zo | =2.6592

critical value

the value of |z | at los 0.025% is 1.96

we got |zo| =2.659 & | z | =1.96

make decision

hence value of | zo | > | z | and here we reject Ho

p-value: right tail - Ha : ( p > 2.65922 ) = 0.00392

hence value of p0.025 > 0.00392,here we reject Ho

ANSWERS

---------------

null, Ho:p=0.2

alternate, H1: p>0.2

test statistic: 2.6592

critical value: 1.96

decision: reject Ho

p-value: 0.00392

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