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3 years ago

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Mathematics

1 answer:

Musya8 [376]3 years ago

5 0

It is 283747489393939

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The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% c

siniylev [52]

Answer:

19 beers must be sampled.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.

This means that $\sigma = 0.26$

If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?

This is n for which M = 0.1. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.1 = 1.645\frac{0.26}{\sqrt{n}}$