In: Statistics and Probability
3. It is suspected that a die is biased in favour of a "6" occurring. The die is thrown 20 times and a "6" is obtained on 6 occasions. Test, at the 5% level of significance, whether there is evidence that the die is biased in favour of a "6".
given data are:-
sample size (n) = 20
sample proportion () = 6/20 = 0.3
hypothesis:-
[ as all the outcomes should be equally likely when you roll a die.]
[ as It is suspected that a die is biased in favor of a "6" occurring ]
test statistic be:-
p value is :-
[ in any blank cell of excel type =NORMSDIST(1.60)]
decision:-
p value = 0.0549 > 0.05 (alpha)
so, we fail to reject the null hypothesis.
conclusion:-
there is not enough evidence to support the suspect that a die is biased in favor of a "6" occurring at 0.05 level of significance.
***in case of doubt, comment below. And if u liked the solution, please like.