In 53 lowerbound percentile 25 resampledmeans upperbound percentile 975

# In 53 lowerbound percentile 25 resampledmeans

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In [53]: lower_bound = percentile( 2.5 , resampled_means) upper_bound = percentile( 97.5 , resampled_means) print ( "95 % c onfidence interval for the average restaurant score, computed by bootstrap 95% confidence interval for the average restaurant score, computed by bootstrapping: ( 90.05 , 92.88 ) Question 4 Does the distribution of the resampled mean scores look normally distributed? State "yes" or "no" and describe in one sentence why you would expect that result. Yes, because the Central Limit Theorem says that the probability distribution of the sum or average of a large random sample drawn with replacement will be roughly normal, regardless of the distribution of the population from which the sample is drawn. Question 5 Does the distribution of the sampled scores look normally distributed? State "yes" or "no" and describe in one sentence why you should expect this result. Hint: Remember that we are no longer talking about the resampled means! No, it’s becuase the Central Limit Theorem does not apply to the distribution of sampled scores. It would only apply to the sum or average of the sampled scores. 7
For the last question, you’ll need to recall two facts. 1. If a group of numbers has a normal dis- tribution, around 95% of them lie within 2 standard deviations of their mean. 2. The Central Limit Theorem tells us the quantitative relationship between the following: * the standard deviation of an array of numbers. * the standard deviation of an array of means of samples taken from those numbers. Question 6 Without referencing the array resampled_means or performing any new simulations, calculate an interval around the sample_mean that covers approximately 95% of the numbers in the resampled_means array. You may use the following values to compute your result, but you should not perform additional resampling - think about how you can use the CLT to accomplish this. In [54]: sample_mean = np . mean(restaurant_sample . column( 3 )) sample_sd = np . std(restaurant_sample . column( 3 )) sample_size = restaurant_sample . num_rows sd_of_means = sample_sd / np . sqrt(sample_size) lower_bound_normal = sample_mean -2* sd_of_means upper_bound_normal = sample_mean +2* sd_of_means print ( "95 % c onfidence interval for the average restaurant score, computed by a normal 95% confidence interval for the average restaurant score, computed by a normal approximation: ( 90.09739258692412 , 92.96260741307589 ) This confidence interval should look very similar to the one you computed in Question 3 . 1.2 2. Testing the Central Limit Theorem The Central Limit Theorem tells us that the probability distribution of the sum or average of a large random sample drawn with replacement will be roughly normal, regardless of the distribution of the population from which the sample is drawn . That’s a pretty big claim, but the theorem doesn’t stop there. It further states that the standard deviation of this normal distribution is given by sd of the original distribution sample size In other words, suppose we start with any distribution that has standard deviation x , take a sample of size n (where n

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