False min sample size is 0 max is 400 the graph will

This preview shows page 9 - 14 out of 32 pages.

False ); # Min sample size is 0, max is 400 # The graph will refresh a few times when you drag the slider around interactive(children=(IntSlider(value=200, description= ' x ' , max=400), Output()), _dom_classes=( You can see that even the means of samples of 10 items follow a roughly bell-shaped distribu- tion. A sample of 50 items looks quite bell-shaped. 9
</div> Question 2: In the plot for a sample size of 10, why are the bars spaced at intervals of .1, with gaps in between?
10
</div> Now we will test the second claim of the CLT: That the SD of the sample mean is the SD of the original distribution, divided by the square root of the sample size. We have imported the flight delay data and computed its standard deviation for you. In [15]: united = Table . read_table( ' united_summer2015.csv ' ) united_std = np . std(united . column( ' Delay ' )) united_std Out[15]: 39.480199851609314 11
</div> Question 3: Write a function called empirical_sample_mean_sd that takes a sample size n as its argument. The function should simulate 500 samples with replacement of size n from the flight delays dataset, and it should return the standard deviation of the means of those 500 samples . Hint: This function will be similar to the sample_size_n function you wrote earlier. In [16]: united Out[16]: Date | Flight Number | Destination | Delay 6/1/15 | 73 | HNL | 257 6/1/15 | 217 | EWR | 28 6/1/15 | 237 | STL | -3 6/1/15 | 250 | SAN | 0 6/1/15 | 267 | PHL | 64 6/1/15 | 273 | SEA | -6 6/1/15 | 278 | SEA | -8 6/1/15 | 292 | EWR | 12 6/1/15 | 300 | HNL | 20 6/1/15 | 317 | IND | -10 ... (13815 rows omitted) In [17]: def empirical_sample_mean_sd (n): sample_means = make_array() for i in np . arange( 500 ): sample = united . sample(n) . column( "Delay" ) sample_mean = np . mean(sample) sample_means = np . append(sample_means, sample_mean) return np . std(sample_means) empirical_sample_mean_sd( 10 ) Out[17]: 12.502203805729613 In [18]: _ = ok . grade( ' q2_3 ' ) _ = ok . backup() ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Running tests --------------------------------------------------------------------- Test summary Passed: 1 Failed: 0 [ooooooooook] 100.0% passed <IPython.core.display.Javascript object> 12
<IPython.core.display.Javascript object> Saving notebook... Saved ' hw09.ipynb ' . Backup... 100% complete Backup successful for user: [email protected] URL: NOTE: this is only a backup. To submit your assignment, use: python3 ok --submit Question 4: Now, write a function called predict_sample_mean_sd to find the predicted value of the standard deviation of means according to the relationship between the standard deviation of the sample mean and sample size that is discussed here in the textbook. It takes a sample size n (a number) as its argument. It returns the predicted value of the standard deviation of the mean delay time for samples of size n from the flight delays (represented in the table united ). In [19]: def predict_sample_mean_sd (n): return united_std / (n) **.5 predict_sample_mean_sd( 10 ) Out[19]: 12.484735400972708 In [20]: _ = ok . grade( ' q2_4 ' ) _ = ok . backup() ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Running tests --------------------------------------------------------------------- Test summary Passed: 1 Failed: 0 [ooooooooook] 100.0% passed <IPython.core.display.Javascript object> <IPython.core.display.Javascript object> Saving notebook... Saved ' hw09.ipynb ' .

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture