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How much money does the average professional hockey fan spend on food at a single hockey​ game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $ 14 and $ 2.70, respectively. Use this information to create a 95% confidence interval for the mean. Express the answer in the form

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Answer:

The confidence interval is

[tex](12.33 ; 15.67)[/tex]

Step-by-step explanation:

Givens

  • The sample mean is 14.
  • The standard deviation is 2.70.
  • The confidence interval is 95%.

To find a confidence interval we have to use the formula

[tex]\mu (+-)z\times \frac{\sigma}{\sqrt{n} }[/tex]

Where [tex]\mu[/tex] is the mean, [tex]z[/tex] is the z-value for a 95% confidence level, [tex]\sigma[/tex] is the standard deviation and [tex]n[/tex] is the sample size.

The z-value for 95% confidence is 1.96.

Replacing all values, we have

[tex]14(+-)1.96\times \frac{2.70}{\sqrt{10} }=14(+-)1.96 \times \frac{2.70}{3.16}=14(+-)1.67[/tex]

Which means the confidence interval is

[tex](14-1.67 ;14+1.67)\\(12.33 ; 15.67)[/tex]

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