Concept 4. Consider the following statement about a 95% confidence interval (CI)

Question

Concept 4. Consider the following statement about a 95% confidence interval (CI) for the parameter and fill in the blank with the correct answer. If the sample size were increased to 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 Circle the letter of the correct statement A BC Concept 5. Consider the following statements for 10 non-negative numbers with mean 100 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. Circle the letter of each statement that is possible and cross out the others: A B CD 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(40x48). Which one? (Hint: It is not necessary to use a normal table to answer this question.) A. P(72

Explanation / Answer

Q4.
increasing the confidence is decreases the margin of error value and this leads to narrower the confidence achived

Q5.
A, C are possibile
B is not possibile, since by assigning three value above 350 and assigning the remaining as 1 also gives the average of minimum 105 which is wrong here
D is not possible, when all the observation below 99, average should definitely less than 99

Q6.

To find P(a < = Z < = b) = F(b) - F(a)
P(X < 40) = (40-60)/10
= -20/10 = -2
= P ( Z <-2) From Standard Normal Table
= 0.0228
P(X < 48) = (48-60)/10
= -12/10 = -1.2
= P ( Z <-1.2) From Standard Normal Table
= 0.1151
P(40 < X < 48) = 0.1151-0.0228 = 0.0923

To find P(a < = Z < = b) = F(b) - F(a)
P(X < 72) = (72-60)/10
= 12/10 = 1.2
= P ( Z <1.2) From Standard Normal Table
= 0.8849
P(X < 80) = (80-60)/10
= 20/10 = 2
= P ( Z <2) From Standard Normal Table
= 0.9772
P(72 < X < 80) = 0.9772-0.8849 = 0.0923

[ANSWER] P(72 < X < 80)

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