BUSI 230 HW 8.1 Confidence Intervals for a Population Mean, Standard Deviation Known Assignment solutions complete answers
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A single number that estimates the value of an unknown parameter is called estimate.
The margin of error is the product of the standard error and the .
In the confidence interval , the quantity is called the .
Find the critical value needed to construct a confidence interval with level 92%.
The critical value for the confidence level is
A sample of size n=61 is drawn from a population whose standard deviation is =34. Find the margin of error for a confidence interval for 90%. Round the answer to at least three decimal places.
The margin of error for a confidence interval for is .
A sample of size n=92 is drawn from a normal population whose standard deviation is =8.3. The sample mean is =38.88.
(a) Construct an 99.5% confidence interval for . Round the answer to at least two decimal places.
(b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain.
How many computers? In a simple random sample of 170 households, the sample mean number of personal computers was 1.31. Assume the population standard deviation is 0.99.
(a) Construct a confidence interval for the mean number of personal computers. Round the answer to at least two decimal places.
A confidence interval for the mean number of personal computers is .
(b) If the sample size were rather than , would the margin of error be larger or smaller than the result in part (a)? Explain.
(c) If the confidence levels were rather than , would the margin of error be larger or smaller than the result in part (a)? Explain.
(d) Based on the confidence interval constructed in part (a), is it likely that the mean number of personal computers is less than ?
Babies: According to a recent report, a sample of 300 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is 5.3 pounds.
(a) Construct a 99.9% confidence interval for the mean weight of all one-year-old baby boys in the United States. Round the answer to at least one decimal place.
(b) Should this confidence interval be used to estimate the mean weight of all one-year-old babies in the United States? Explain.
(c) Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is greater than pounds?
How smart is your phone? A random sample of Samsung Galaxy smartphones being sold over the Internet in had the following prices, in dollars:
(a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.
(b) Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal?
(c) If appropriate, construct a 95% confidence interval for the mean price for all phones of this type being sold on the Internet in 2013. Round your intermediate step to three decimal places. Round your answer to one decimal place.
