For hypothesis tests, please give me the null and alternative hypotheses, the fo

Question

For hypothesis tests, please give me the null and alternative hypotheses, the formula for the test statistic, the appropriate substitutions, the value of the test statistic, the rejection region (be careful on two-sided tests, don’t forget both tails) or p-value (Note: This means you can use either approach, unless specified), whether you accept or reject the null, and the interpretation of the results in the words of the problem.

For confidence and prediction intervals, give the formula used for the interval, the appropriate substitutions, the actual interval(s), and interpret it in the context of the problem.

1 You roll a die 48 times with the following results.

Number:    1    2    3 4    5    6

Frequency: 13 2    3    13 13    4

Do the data provide sufficient evidence to conclude that the die is loaded (i.e., that the six numbers are not equally likely)? Test at the 0.05 level of significance.

Explanation / Answer

Ans:

Chi square test:

H0:Six numbers are equally liekely.(die is not loaded)

H1:Six numbers are not equall likely.(die is loaded)

Test statistic:

Total Calculated Chi square score=19

df=6-1=5

p-value=CHIDIST(19,5)=0.001922

Significance level=0.05

As,p-value<0.05,Reject Null hypothesis,H0.

There is sufficient evidence to conclude that Six numbers are not equall likely(die is loaded)

1 2 3 4 5 6 Total Observed(O) 13 2 3 13 13 4 48 Expected(E) 8 8 8 8 8 8 48 (O-E)^2/E 3.125 4.5 3.125 3.125 3.125 2 19

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