# Question about a statistics problem

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Lingbai Ren on 16 Oct 2020
Commented: Lingbai Ren on 16 Oct 2020
I have done part a to c, got stuck on part d
the description of part a, b, and c is below:
(a) Begin by writing a script that will generate 500 samples drawn from a uniform distribution. We want to implement a true proportion of 0.7 (e.g., 70% of people are in favor of some new law). In the end, you should have an array filled with 1’s and 0’s, where any random number between 0 and 0.7 is assigned a 1, and any random number between 0.7 and 1 is assigned a 0.
(b) Write a script that will compute the proportion of the sample from part (a), which is an estimate of the true proportion. Use it to verify that you did part (a) correctly; the estimate should be fairly close to the true value.
(c) Write a script that computes the standard error of the estimate of the proportion. You must pretend that you don’t know the true proportion, so must use the estimate.
For part d, I was asked to construct a for loop to loop through step a to c 1000 times, each time through, I will take 500 smaples and estimate the proportion. In the end, I will have an array of 1000 estimates. I will also have an array of 1000 associated standard errors of the estimates.
I am assuming we are using nested for loop in this case, but I kept getting "number of success" as single value in script. I attached my code below, please help me to check where I did wrong!
%% (d) Construct a for loop to loop through (a) through (c) 1000 times
clc,clear
loop_times = 1000;
sample_size = 500;
number_of_success = 0; % number of success counter
u = rand(sample_size,1); % Generate 500 samples from a uniform distribution
trueVal = 0.7;
for k = 1:loop_times
for i = 1:sample_size
if u(i)<trueVal && u(i)>0
u(i) = 1; % Assign 1 to numbers between 0 and 0.7
number_of_success = number_of_success + 1;
else
u(i) = 0; % Assign 0 to numbers between 0.7 and 1
end
end
end
estimate_sample_proportion = number_of_success/sample_size;
standard_error = sqrt((estimate_sample_proportion * (1 - estimate_sample_proportion))...
/ sample_size)
Lingbai Ren on 16 Oct 2020
So, I think what Matt provided helped a lot!
Now I am worrying about another part of the problem:
(f). Construct a second FOR loop script that determines the ratio of the estimates for which the true proportion falls within the 95% confidence interval of each of the estimates. If you’ve done it correctly, you should find that the true proportion was within the confidence interval for approximately 95% of your estimates.
I am a little bit confused what are we trying to find? Is it the ratio of the estimates? And will that be a single value or will be an array? Could anyone goot at Statistics help?
Here is what I got:
%% (d) Construct a for loop to loop through (a) through (c) 1000 times
clc,clear
loop_times = 1000;
sample_size = 500;
% number of success counter
u = rand(sample_size,loop_times); % Generate 500 samples from a uniform distribution
trueVal = 0.7;
number_of_success = sum(u<trueVal);
for k = 1:loop_times
for i = 1:sample_size
if u(i)<trueVal && u(i)>0
u(i) = 1; % Assign 1 to numbers between 0 and 0.7
number_of_success = number_of_success + 1;
else
u(i) = 0; % Assign 0 to numbers between 0.7 and 1
end
end
end
estimate_sample_proportion = number_of_success/loop_times; %array of 1000 estimates
standard_error = sqrt((estimate_sample_proportion .* (1 - estimate_sample_proportion))...
/ loop_times) % array of 1000 standard errors
% (f) Construct a second for loop to determind the ratio of the estimates
for j = 1: length(estimate_sample_proportion)
ratio_of_estimates = (estimate_sample_proportion(j) + 1.96 * standard_error(j)...
+ (estimate_sample_proportion(j) - 1.96 * standard_error(j)))/1
end

Matt J on 16 Oct 2020
I think you should just do,
u = rand(sample_size,loop_times);
number_of_success = sum(u<trueVal)

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