Question

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 standard deviation s = 15 hours. A sample of 45 cell phones has a mean time of 145 hours. Let m represent the population mean time that

a cell phone will keep a charge.
a. What is the point estimate of m ?

b. What is the standard error of the point estimate? Round to three decimal places.

c. Suppose that a 90% confidence interval is to be constructed for the mean time. Find the margin of error for this confidence interval (use three decimal places).

e. Construct the 90% confidence interval and interpret your result:

f. What sample size would be necessary so that a 98% confidence interval will have a margin of error of 2 hours?

Solutions

Expert Solution

Solution:

a. What is the point estimate of m?

Answer: The point estimate of m is:

b. What is the standard error of the point estimate? Round to three decimal places.

Answer: The standard error of the point estimate is:

c. Suppose that a 90% confidence interval is to be constructed for the meantime. Find the margin of error for this confidence interval (use three decimal places).

Answer: The 90% confidence interval for the mean time is:

Where:

     

e. Construct the 90% confidence interval and interpret your result:

Answer: The 90% confidence interval is:

f. What sample size would be necessary so that a 98% confidence interval will have a margin of error of 2 hours?

Answer: The formula for finding the sample size is:

Where:

  

    

orchestra answered 1 year ago
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