Question
In: Statistics and Probability
The average selling price of a smartphone purchased by a random sample of 37 customers was...
The average selling price of a smartphone purchased by a random sample of 37 customers was $314. Assume the population standard deviation was $35.
a. Construct a 95% confidence interval to estimate the average selling price in the population with this sample.
b. What is the margin of error for this interval?
a. The 95% confidence interval has a lower limit of $ and an upper limit of $ . (Round to the nearest cent as needed.)
b. The margin of error is $ . (Round to the nearest cent as needed.)
Solutions
Expert Solution
a. Construct a 95% confidence interval to estimate the average selling price in the population with this sample.
We need to construct the 95% confidence interval for the population mean . The following information is provided:
| Sample Mean | 314 |
| Population Standard Deviation | 35 |
| Sample Size | 37 |
The critical value for α=0.05 is z_c = 1.96 . The corresponding confidence interval is computed as shown below:
b. What is the margin of error for this interval?
Margin of error = Length of confidence interval / 2
Length of confidence interval = 325.278 - 302.722 = 22.556
Margin of error = 22.556/2 = 11.278
a. The 95% confidence interval has a lower limit of $ and an upper limit of $ . (Round to the nearest cent as needed.)
b. The margin of error is $ . (Round to the nearest cent asneeded.)
Margin of error = Length of confidence interval / 2
Length of confidence interval = 325 - 303 = 22
Margin of error = 22/2 = 11
orchestra answered 1 year agoRelated Solutions
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