Question

in a random sample of six cell phones, the mean full retail price was $579.00 and the standard deviation was $210.00. assume the population is normally distributed and use the t - distribution to find the margin of error and construct a 99% confidence interval for the population mean μ. interpret the results.

identify the margin of error.
345.8 dollars
(round to one decimal place as needed.)

construct a 99% confidence interval for the population mean.
(233.2, 924.8)
(round to one decimal place as needed.)

interpret the results. select the correct choice below and fill in the answer box to complete your choice.
(type an integer or a decimal. do not round.)

○ a. □% of all random samples of six people from the population of cell phones will have a mean full retail price (in dollars) that is between the intervals endpoints.
○ b. with □% confidence, it can be said that most cell phones in the population have full retail prices (in dollars) that are between the intervals endpoints.
○ c. with □% confidence, it can be said that the population mean full retail price of cell phones (in dollars) is between the intervals endpoints.
○ d. it can be said that □% of the population of cell phones have full retail prices (in dollars) that are between the intervals endpoints.

Explanation:

A confidence interval gives an estimated range for the population parameter (here, the population mean). A 99% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, approximately 99% of those intervals would contain the true population mean.

• Option A is incorrect because it refers to the proportion of samples with means in the interval, not about the population mean.
• Option B is wrong as it talks about most cell - phones (individual values), while the confidence interval is about the population mean.
• Option D is incorrect as it refers to the proportion of the population (individual values) rather than the population mean.
• Option C is correct as it correctly states that with 99% confidence, the population mean is within the interval endpoints.

Answer:

C. With 99% confidence, it can be said that the population mean full retail price of cell phones (in dollars) is between the interval's endpoints.