Question

Concept 4. Consider the following statement about a 95% confidence interval (CI) for the parameter p and enter the correct answer for the blank. If the sample size were increased to n 1000 then the confidence interval would be the confidence interval computed from a sample with n 64. A. Narrower than B. Wider than C. The same size as Concept 5. Consider the following statements for 10 non-negative numbers with mean 100. Select the letter(s) of each statement that is possible: A. Three of these numbers are greater than 330. B. Three of these numbers are greater than 350. C. All 10 numbers are less than 110. D. All 10 numbers are less than 99 Concept 6. The random variable X has a Normal distribution with mean 60 and standard deviation 10. One of the following probabilities is the same as P(40 <X<48). Which one? (Hint: It is not necessary to use a normal table to answer this question.) A. P(72<X<80) B. P(56 <X64) C. P(50<X<58) D. P(80<X <88) E. P(64<X < 72) t natients in medical offices and requested

Answer 1

4) The 95% confidence interval is given by .

7-1.96-n<p<T+1.96v n

The width of the 95% CI is
2 × 1.96-n
. Clearly width decreases as increases.

Correct choice is A) Narrower than

5) The possible scenarios are

A)3 of thses 10 numbers are greater than 330. So the numbers can be 331,331,331,1,1,1,1,1,1,1

C) All 10 numbers are less than 110.

6) The normal distribution is symmetric about mean. Here $\mu =60$. So beacuse of symmetry,

P(40< X < 48) -P(60 + 12< X< 60 20) P(40 〈 X 〈 48) = P(72 〈 X 〈 80)

Here 40 corresponds to 80 on the right side of mean.

48 corresponds to 72 on the right side of mean.

A) is the correct choice