Answer:
(a) The standard error of estimate of the fraction of blue cards in the deck is 0.145.
(b) The sample size required is 84.
Step-by-step explanation:
The proportion of blue cards is, <em>p</em> = 0.30.
The number of times the cards were shuffled is, <em>n</em> = 10.
(a)
The standard error for sample proportion is given by:
Compute the value of standard error as follows:
Thus, the standard error of estimate of the fraction of blue cards in the deck is 0.145.
(b)
Now we need to reduce the standard error.
The standard error is inversely proportional to the sample size.
If the sample size is increased then the standard error will be decreased.
So we need to use a larger sample size.
Compute the value of <em>n</em> for standard error 0.05 and <em>p</em> = 0.30 as follows:
Thus, the sample size required is 84.