HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 147

23 THE EXPERT: CHI2 TESTS & FREQUENCY TABLES We will start with a small digression to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets. Using the Chi2 test on a frequency table "Four coins are tossed 400 times and the number of heads noted for each toss. The results are shown below. Using the Chi2 test at a 5% level of confidence, indicate whether the coins may be biased." Number of heads Frequency 0 1 2 3 4 32 112 158 90 8 We would expect that for an un-biased set of coins the distribution would be binomial. Our hypotheses are: H0: The number of heads is binomially distributed (n=4 & p=0.5) HA: The number of heads is not binomially distributed (n=4 & p=0.5) Begin by entering the data into the first two columns of the Statistics aplet (right). We now need to calculate the expected values based on our null hypothesis. The expected values are based on the assumption that the results are binomially distributed with n=4 and p=0.5. We can do this in the HOME view using the calculation shown right (and below), inserting the results into column C3 using the button. 400*COMB(4,C1)*.5^C1*.5^(4-C1) C3 We can now calculate the X2 value as the sum of the values in column C4 using the ∑LIST function. The calculations are shown right, placing the individual values into column C4 for inspection if required and then finding the sum of the column. The values can be seen by changing to the NUM view. 147