The following table contains the observed distribution of the last digit of the

Question

The following table contains the observed distribution of the last digit of the forecasted high temperature on a certain day for n = 150 cities.

(a) Compute expected counts for the null hypothesis that all digits 0, 1, ..., 9 are equally likely to be the last digit of the forecasted high temperature.

(b) Calculate the chi-square goodness-of-fit statistic, 2, for these data. (Give the answer correct to three decimal places.)
2 =  

What are the degrees of freedom, df, for this statistic?
df =  

(c) State a conclusion about the null hypothesis that all digits are equally likely to be the last digit selected.
---Select--- Do not reject Reject the null hypothesis. There  ---Select--- is is not statistically significant evidence against the hypothesis that all digits are equally likely to be the last digit of the forecasted high temperature.

Last Digit 0 1 2 3 4 5 6 7 8 9 Count 10 19 9 23 8 18 14 16 15 18

Explanation / Answer

putt expected count =150/10 =15 in each cell

applying chi square goodness of fit test:

b)2 = 14

df =categories-1 =9

c) Do not reject  null hypothesis. There is not statistically significant evidence against the hypothesis that all digits are equally likely to be the last digit of the forecasted high temperature.

observed Expected residual Chi square x Probability(p) Oi Ei=total*p Ri=(Oi-Ei)/Ei R2i=(Oi-Ei)2/Ei 0 1/10 10.000 15.0 -1.29 1.67 1 1/10 19.000 15.0 1.03 1.07 2 1/10 9.000 15.0 -1.55 2.40 3 1/10 23.000 15.0 2.07 4.27 4 1/10 8.000 15.0 -1.81 3.27 5 1/10 18.000 15.0 0.77 0.60 6 1/10 14.000 15.0 -0.26 0.07 7 1/10 16.000 15.0 0.26 0.07 8 1/10 15.000 15.0 0.00 0.00 9 1/10 18.000 15.0 0.77 0.60 total 1 150 150 0 14.000

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