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A research firm conducted a survey to determine the mean amount Americans spend on coffee during a week. They found the distribution of weekly spending followed the normal distribution with a population standard deviation of $5. A sample of 64 Americans revealed that X¯¯¯=$20 . What is the 95% confidence interval estimate of μ?

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Answer:

95% confidence Interval would be between $18.775 and $20.225.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

  • M is the sample mean Americans spend on coffee during week. ($20)
  • ME is the margin of error from the mean

And margin of error (ME) around the mean calculated as

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

  • z is the corresponding statistic in 95% confidence level (1.96)
  • s is the population standard deviation ($5)
  • N is the sample size (64)

Using the numbers, we get:

ME=[tex]\frac{1.96*5}{\sqrt{64} }[/tex] =1.225

Then 95% confidence Interval would be 20±1.225 or between $18.775 and $20.225

Answer:

The confidence interval is between 18.775 and 21.225.

Step-by-step explanation:

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