Use the chi-square goodness-of-fit test to determine whether this distribution i
ID: 3305179 • Letter: U
Question
Use the chi-square goodness-of-fit test to determine whether this distribution is significantly different from the normal distribution. Assume that = .025.
19
a)what is chi square(x2)= -------------------------------(*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)
b) is it < 0r >
c) what is the value of X2 .025,3 = ------------------------- (**Round your answer to 4 decimal places when calculating using Table A.8)
d) do we reject of fail to reject null value
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 7019
Explanation / Answer
FIrst to check normality assumption we will calculate mean and standard deviation of the given frequncy distribution.
Mean xbar = xf/ x = 9155/231 = 39.63
Varaince = xf2 /n -x2bar = 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)
(a) what is chi square(x2)= 2.35
(b0 IT is less than the critical value of chi - square.
(c) X2.025,3 = 9.348
(d) p - value = 0.7988
(d) So, we fail to reject the null hypothesis and can conclude that the data is normal.
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 405375Related Questions
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