Respuesta :
Answer:
15 dog heights; [tex]n=15[/tex]
Step-by-step explanation:
The formula to be used here is [tex]MOE_\gamma=z_\gamma*\sqrt{\frac{\sigma}{n} }[/tex] where:
- [tex]\gamma[/tex] is the confidence level
- [tex]MOE_\gamma[/tex] is the margin of error for a confidence level
- [tex]z_\gamma[/tex] is the critical value for the confidence level
- [tex]\sigma[/tex] is the population standard deviation
- [tex]n[/tex] is the sample size
We are given that:
- [tex]\gamma=0.95[/tex]
- [tex]MOE_\gamma=1[/tex]
- [tex]z_\gamma=invNorm(0.975,0,1)=1.96[/tex]
- [tex]\sigma=3.7[/tex]
To determine the minimum sample size, [tex]n[/tex], we plug our given values into the formula and solve for
[tex]MOE_\gamma=z_\gamma*\sqrt{\frac{\sigma}{n} }[/tex]
[tex]1=1.96\sqrt{\frac{3.7}{n} }[/tex]
[tex]\frac{1}{1.96}=\sqrt{\frac{3.7}{n} }[/tex]
[tex](\frac{1}{1.96}) ^{2}=\frac{3.7}{n}[/tex]
[tex]n=\frac{3.7}{(\frac{1}{1.96})^{2} }[/tex]
[tex]n=14.21392[/tex]
Don't forget to round up here! This means that [tex]n=15[/tex] actually.
Therefore, if we want to be 95% confident that the sample mean is within 1 inch of the true population mean, the minimum sample size that can be taken is 15 dog heights.
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