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Arte-miy333 [17]
3 years ago
10

One of the more famous anecdotes in the field of statistics is known as the "Lady Tasting Tea" and involves the renowned statist

ician Sir Ronald Aylmer Fisher. A woman claimed to be able to tell the difference in a cup of tea depending on whether or not the milk or tea was poured first. You have chosen to recreate this experience with a classmate and have fixed 40 cups of tea, of which your classmate correctly identifies 12. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.30 as the value for p. n = 42 n = 81 n = 4116 n = 8068
Mathematics
1 answer:
mote1985 [20]3 years ago
7 0

Answer:

n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36  

And rounded up we have that n=8068

Step-by-step explanation:

The margin of error for the proportion interval is given by this:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

We want for this case a 95% of confidence desired, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The margin of error for this case is ME =\pm 0.01 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

The estimated proportion for this case is \hat p=0.3. And replacing into equation (b) the values from part a we got:

n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36  

And rounded up we have that n=8068

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