When a certain international spin bowler has bowled a slow full toss in one day

Question

When a certain international spin bowler has bowled a slow full toss in one day matches in previous seasons, the outcomes (5 possible outcomes in total) have appeared in the proportions according to the table below 4 runs 0.25 1-3 runs 0.15 6 runs wicket Outcome Proportion 0.30 During the current season the scorer has recorded that the bowler has bowled a total of 80 full tosses with the frequency of results shown in the table below. 4 runs -3 runs Outcome 6 runs No. of times o runs 12 wicket 21 35 (a) What proportions of the time is the outcome "wicket? (b) Assuming the batsman is handling this bowler's slow full tosses similarly to previous seasons determine the expected frequency of results. Outcome Proportion Expected Frequency 6 runs 4 runs 1-3 runs 0 runs wicket Total 0.20 0.25 0.15 0.30 (c) If we want to perform a hypothesis testing to determine whether the batsmen seem to be handling this bowler's slow full tosses differently than in previous seasons, what are the null and alternative hypotheses? (d) What would be an appropriate statistical test for this hypothesis testing?

Explanation / Answer

a) The proportion of time is the outcome "wicket" is 0.10
since sum of probabilities are equal to 1

b) From the given data

c)
H0:The batsman seem to be handling this bowler's slow full tosses differently than in previous seasons.
H1: The batsman seem to be handling this bowler's slow full tosses not differently than in previous seasons..

d)

Num Categories: 5
Degrees of freedom: 4

Test Statistic, X^2: 22.6875
Critical X^2: 9.48772
P-Value: 0.0001

Here chisquare value > chisquare critical value and P-value < alpha 0.05 so we reject H0

Thus we conlcude that the batsman seem to be handling this bowler's slow full tosses not differently than in previous seasons..

Observed Expected Grades Freq (Oi) Probability Freq Ei 6runs 21 0.2 16 4runs 35 0.25 20 1-3 runds 9 0.15 12 0 runs 12 0.3 24 wicket 3 0.10 8 Total: 80 1.00 80

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