## An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line at their site. A consumer group is

Question

An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line at their site. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%. A random sample of 80 graduate students show that only 44 students have ever done so. Is there enough evidence to show that the true proportion is lower than 60%? Assume that significance level of 0.05. Use the hypothesis testing template provided.’

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2021-11-20T19:41:01+00:00
2021-11-20T19:41:01+00:00 1 Answer
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## Answers ( )

Answer:We accept H₀ we don´t have enough evidence to conclude that a consumer group position is correctStep-by-step explanation:We have a case of test of proportion, as a consumer group is suspicious of the claim and think the proportion is lower we must develop a one tail test (left tail) Then1.- Test hypothesis:Null hypothesis H₀ P = P₀Alternative hypothesis Hₐ P < P₀2.- At significance level of α = 0,05 Critical valuez(c) = -1,643.-We compute z(s) value as:z(s) = ( P – P₀ )/ √P*Q/n where P = 44/80 P = 0,55 and Q = 0,45P₀ = 0,6 and n = 80Plugging all these values in the equation we get:z(s) = ( 0,55 – 0,6 ) / √(0,2475/80)z(s) = – 0,05/ √0,0031z(s) = – 0,05/0,056z(s) = – 0,89284.-We compare z(s) and z(c)z(s) > z(c) -0,8928 on the left side it means that z(s) is in the acceptance region so we accept H₀