Finding the p-value with the z-statistic


                    # This will get executed each time the exercise gets initialized.

                    import numpy as np
                    import pandas as pd
                    import scipy.stats as stats
                    
                    x = np.array(['R','R','R','R','R','R']*10)
                    
                    n = len(x)
                    N = 1000
                    counts = np.random.binomial(n,0.5,N)
                    phat = counts/n


                    # libraries
                    import numpy as np
                    import pandas as pd
                    import scipy.stats as stats
                    
                    # initialization code
                    dataphat = len(x[x == 'R'])/n
                    phatdf = pd.DataFrame(phat, columns = ['phat'])
                    meandist = phatdf['phat'].mean()
                    SEdist = phatdf['phat'].std()
                    
                    # calculate z-statistic
                    z = ...
                    
                    # left-tailed test 
                    print('left-tailed p-value: ', stats.norm.cdf(...))
                    
                    # right-tailed test
                    print('right-tailed p-value: ', stats.norm.cdf(...))


                    # libraries
                    import numpy as np
                    import pandas as pd
                    import scipy.stats as stats
                    
                    # initialization code
                    dataphat = len(x[x == 'R'])/n
                    phatdf = pd.DataFrame(phat, columns = ['phat'])
                    meandist = phatdf['phat'].mean()
                    SEdist = phatdf['phat'].std()
                    
                    # calculate z-statistic
                    z = (dataphat - 0.5)/SEdist
                    
                    # left-tailed test 
                    print('left-tailed p-value: ', stats.norm.cdf(z))
                    
                    # right-tailed test
                    print('right-tailed p-value: ', stats.norm.cdf(-1*z))