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Weather Forecasters Would Like to Report on Temperatures in Washington

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Weather forecasters would like to report on temperatures in Washington, DC. In particular, they would like to compare the temperatures in December to temperatures in January to help potential tourists understand whether there is a difference. The average December temperature in a random sample of 16 days is 35 and the average January temperature in a random sample of 20 days is 33. The standard deviations based on historic information are 4 for December and 5 for January.
A) Construct a 90% confidence interval for the difference between the population mean temperatures in December and January.
B) Can we conclude with 90% confidence that the mean temperatures in December and January are different?


Definitions:

Microorganisms

Very small, often single-celled organisms that can be bacteria, fungi, viruses, or protozoa, not visible to the naked eye.

Iron Formation

A sedimentary rock consisting of alternating layers of iron-rich minerals and silica or carbonate, typically formed in Precambrian seas.

Seawater

The saltwater that makes up the oceans and seas, covering more than 70% of the Earth's surface, containing various salts and life forms.

Silica-rich Organisms

Organisms that produce silica (silicon dioxide) as part of their structure, such as diatoms and certain sponges.

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