Question

78% of all Millennials drink Starbucks coffee at least once a week. We speculate that this rate is lower among teenager in the US. A random sample of 40 teenagers was randomly selected and 60% said that they drink Starbucks coffee at least once a week. What distribution would you use to assess if the proportion of teenagers in the US who drink Starbucks coffee at least once a week is less compared to Millennials?

Answer 1

According to the sample size, it will be necessary to approximate the data through the normal distribution and through this calculate the standard deviation to obtain both the average, the standard deviation and the obtained deviation. Here the sample size is 40.

Approximately the distribution of proportion is a Normal distribution using the CLT. the mean will be 0.78, then we have that the standard deviation is,

$\sigma = \sqrt{\frac{p(1-p)}{n}}$

$\sigma = \sqrt{\frac{(0.78)(0.22)}{40}}$

$\sigma = 0.0655$

Then the distribution will be normal with the values of 0.78 to 0.0655 for the mean and the standar deviation respectively.

Normal (0.78,0.0655)