A recent poll was conducted where 97% responded \"yes\" when posed the question

Question

A recent poll was conducted where 97% responded "yes" when posed the question "after using the restroom. do you always wash your hands?" Researchers, posing as bathroom attendants, monitored 18 people, randomly selected in the bathroom. Of those 18 people, only 12 washed their hands before leaving the restroom. A Do these data provide convincing evidence that less than 97% of people wash their hands after using the bathroom? Carry out a hypothesis test with a CI-95%. Be sure to state the null and alternate hypotheses, critical t value and B If these data show, that less than 97% of people wash their hands, where the people polled lying? Explain your answer.

Explanation / Answer

A) H0: p = 0.97

H1: p < 0.97

sample proportion, p = 12/18 = 0.667

Decision rule : If Z statistic < -1.645, then reject H0

Z test statistic = p -P / (PQ/n)±

= 0.667 - 0.97 / (0.97*0.03/18)

= -7.575

Here Z statistic < -1.645, Reject H0

b) No, People are not lying, since we infer that there is sufficient evidence of that the proportion is less than 97%

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