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In: Statistics and Probability

The amount of time that a certain cell phone will keep a charge is known to...

The amount of time that a certain cell phone will keep a charge is known to be normally distributed with a population standard deviation of 16 hours. A sample of 40 cell phones had a mean time of 141 hours. Let u represent the population mean time that a cell phone will keep a charge. a. What is the critical value given a 95% confidence interval is to be constructed for the mean time? b. What is the margin of error? c. What sample size is necessary so that a 95% confidence interval will have a margin of error of 1 hour? d. Construct the 95% confidence interval

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Expert Solution

The provided sample mean is 141 and the population standard deviation is σ=16. The size of the sample is n = 40 and the required confidence level is 95%.

a. What is the critical value given a 95% confidence interval is to be constructed for the mean time?

Based on the provided information, the critical z-value for α=0.05 is z_c = 1.96

b. What is the margin of error?

c. What sample size is necessary so that a 95% confidence interval will have a margin of error of 1 hour?

.

n = 983.4496

n = 984

d. Construct the 95% confidence interval


CI =(136.042,145.958)

which completes the calculation.

orchestra answered 1 year ago
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