Question about a statistics problem

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]

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

Answer 1

[Matt J]

I think you should just do,

u = rand(sample_size,loop_times);

number_of_success = sum(u<trueVal)