O Question The CenausAlschool data set contains results from a Murvey question i

Question

O Question The CenausAlschool data set contains results from a Murvey question in which war askal decimal places, ae shown in the table below. requency table results for Eaverite SeaM: Count 450 Relative Frequescy Favorite season Sprang However, what if we are only interested in the percent of students who stated summu was table is that favorite season. Now, there are only two possible responses, Summer or Not summmer The fevised shown below. Relative Frequency Frequency Favorite Season Not Summer la We are planning to select 40 people from our data set. Calculate by hand' the standard emor for the proportion of people who stated that was their favorite season in a sample ofsize 40 Show work Sgsmer decimal places. including the formula and round your answer to four

Explanation / Answer

1.a Standard Error for sample proportion = sqrt [ p( 1-p)/n)] = sqrt [ 0.29 * 0.71 /40] = 0.0717

1.d. Standard deviation found in the output of 1000 simulations = 0.0701

and calculated in question 1.a , std. deviation = 0.0717

so , we can say that standard deviation are similar in both cases as calculated by simulation or when calculated by formula. If we compare both standard deviation, there is only ( 0.0717 - 0.0701)/0.0716 = 2.2% error or difference.

1.e. the shape of the graph for sample population through simulation has normal distribution and its mean is 0.2916 which is very close to the given mean = 0.29 , if we compare both means , it will give only (0.2916 - 0.29)/ 0.29 = 0.55% error which is very low so results from the simulation have produced very accurate results.

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