Question

The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task, occasional red and green lights flashed on the computer screen. If a green light flashed, subjects were to continue driving, but if a red light flashed, subjects were to brake as quickly as possible. The reaction time (in msec) was recorded. The following summary statistics are based on a graph that appeared in the paper. n = 61 x = 530 s = 75 (a) Assuming that this sample is random/representative of the population, what other assumptions need to be true before we can create a confidence interval? Yes, because the population distribution is normal. No, because n < 30 No, because either np̂ < 10 or n(1−p̂) < 10 Yes, because np̂ ≥ 10 and n(1−p̂)≥ 10 Yes, because n ≥ 30 No, because the population distribution is not normal. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) Construct a 98% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.) , (c) Interpret a 98% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. We are % confident that the mean time to react to a is between and milliseconds. (d) Suppose that the researchers wanted to estimate the mean reaction time to within 5 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size. (Round your answer up to the nearest whole number.) n = You may need to use the appropriate table in Appendix A to answer this question.

Answer 1

(a) Assuming that this sample is random/representative of the population, what other assumptions need to be true before we can create a confidence interval?

Yes, because the population distribution is normal.

(b) Construct a 98% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.)

507.048 to 552.952

(c) Interpret a 98% confidence interval for μ, the mean time to react to a red light while talking on a cell phone.

We are 98% confident that the mean time to react to a is between 507.048 and 552.952 milliseconds.

(d) Suppose that the researchers wanted to estimate the mean reaction time to within 5 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size. (Round your answer up to the nearest whole number.)

n = 865

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