Questions 14-17 are based on the following information Among all adult Indiana r
ID: 3174790 • Letter: Q
Question
Questions 14-17 are based on the following information
Among all adult Indiana residents 85% are high school graduates. Answer questions 14-17 based on sampling distribution of P for random samples of n=520 Indiana residents.
14.) The fraction of sample proportions obtained from samples of size n=520 that fall between +-0.04 (4 percentage points) from the population porportion PIE is ___
15.) The fraction of sample proportions obtained from samples of size n = 750 that fall within ±0.03 (3 percentage points) from is _________.
16.)The lower and upper ends of the interval which contains the middle 95% of all sample proportion obtained from samples of size n = 600 are: p = _______, p = _______
A.) 0.835;0.865
B.) 0.831;0.869
C.) 0.821;0.879
D.) 0.812;0.888
17.) In the previous question, in order the obtain a margin of error of ±0.02 (MOE = 0.02) for the middle interval that contains the middle 95% of all sample proportions, the minimum sample is: n = ______.
A.) 1225
B.) 1245
C.) 1265
D.) 1285
0.9476Explanation / Answer
Result:
Questions 14-17 are based on the following information
Among all adult Indiana residents 85% are high school graduates. Answer questions 14-17 based on sampling distribution of P for random samples of n=520 Indiana residents.
14.) The fraction of sample proportions obtained from samples of size n=520 that fall between +-0.04 (4 percentage points) from the population porportion PIE is ___
0.9476
0.9742
Answer: 0.9892
0.9938
n=520, standard error =sqrt(0.85*0.15/520) =0.0157
z=0.04/0.0157 =2.55
fall between +-0.04 = P( -2.55<z<2.55) = P( z <2.55) – P( z < -2.55)
=0.9946-0.0054 =0.9892
15.) The fraction of sample proportions obtained from samples of size n = 750 that fall within ±0.03 (3 percentage points) from is _________.
Answer: 0.9792
0.9452
0.9232
0.8764
n=750, standard error =sqrt(0.85*0.15/750) =0.0130
z=0.03/0.0130=2.31
fall between +-0.03 = P( -2.31<z<2.31) = P( z <2.31) – P( z < -2.31)
=0.9896-0.0104=0.9792
16.)The lower and upper ends of the interval which contains the middle 95% of all sample proportion obtained from samples of size n = 600 are: p = _______, p = _______
A.) 0.835;0.865
B.) 0.831;0.869
Answer: C.) 0.821;0.879
D.) 0.812;0.888
Confidence Interval Estimate for the Proportion
Data
Sample Size
600
Number of Successes
510
Confidence Level
95%
Intermediate Calculations
Sample Proportion
0.85
Z Value
1.9600
Standard Error of the Proportion
0.0146
Interval Half Width
0.0286
Confidence Interval
Interval Lower Limit
0.821
Interval Upper Limit
0.879
17.) In the previous question, in order the obtain a margin of error of ±0.02 (MOE = 0.02) for the middle interval that contains the middle 95% of all sample proportions, the minimum sample is: n = ______.
Answer: A.) 1225
B.) 1245
C.) 1265
D.) 1285
1.96*sqrt(0.85*0.15/n) =0.02
0.85*0.15/n=0.02^2/1.96^2
n=1224.5 = 1225( rounded)
0.9476
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