The general manager of an AFL team believes the ages of purchasers of game ticke

Question

The general manager of an AFL team believes the ages of purchasers of game tickets are normally distributed. The following data represent the distribution of ages for a sample of observed purchasers of AFL game tickets. Use the chi-square goodness-of-fit test to determine whether this distribution is significantly different from the normal distribution. Assume that = .1.

*Round the values of probablities to 4 decimal places. Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places, the tolerance is +/-0.05.
**Round your answer to 4 decimal places when calculating using Table A.8.

.

Age of Purchaser Frequency 10–under 20 16 20–under 30 44 30–under 40 61 40–under 50 56 50–under 60 35 60–under 70 19

Explanation / Answer

THe table below is given that for the calculation of Mean and standard deviation of the given distribution

MEan = 9155/231 =  39.63

Varaince = 405375/231 - (39.63)2 = 184.33

Standard deviation = 13.60

so Now we have Mean and standard deviation of the given frequency distribution. Now we willl check its normality.

We will use excel here to do the calculation .

The formula of functions used is NORMDIST(X, 39.63, 13.60, True) For cumulative probability. Where X is the upper range of the interval.

Group Interval probability can be calculated by NORMDIST(Xn, 39.63, 13.60, True) -  NORMDIST(Xn-1, 39.63, 13.60, True)

Expected frequency can be calculated by multiplication by 231.

Chi -square is the sum of all values which is 2.35

Critical value X2 = CHIINV (0.1, dF) = CHIINV (0.1, 5)

P - value = CHITEST (Observed Range, Expected Range)

X2(0.1,3) = 11.334

so here we can see thaat X2 = 2.35 < critical chi - square value so we can say that the data is normal as we can not reject the null hypothesis.

Group Interval Midpoint (x) Frequeny (f) xf fx^2 10-20 15 16 240 3600 20 -30 25 44 1100 27500 30-40 35 61 2135 74725 40-50 45 56 2520 113400 50-60 55 35 1925 105875 60-70 65 19 1235 80275 Sum 231 9155 405375

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