A six sided die is rolled 120 times Fill in the expected frequency column Then, conduct a hypothesis test at the 5 level to determine if the die is fair The data below are the result of the 120 rolls (Enter exact numbers as integers, fractions, or decimals ) Be Careful with the rounding be sure to use all Face Value Frequency Expected Frequency 1 14 2 32 3 15 4 14 5 31 6 14 Part (a) Multiple Choice State the null hypothesis a) The data fit the distribution for a fair six sided die b) The data do not fit the distribution for a fair six sided die Part (b) Multiple Choice State the alternative hypothesis a) The data do not fit the distribution for a fair six sided die b) The data fit the distribution for a fair six sided die Part (c) What are the degrees of freedom (Enter an exact number as an integer, fraction, or decimal ) Part (d) Multiple Choice State the distribution to use for the test a) 26 b) t 6 c) t 5 d) 25 Part (e) What is the test statistic (Round your answer to two decimal places ) Part (f) What is the p value (Round your answer to four decimal places ) P Explain what the p value means for this problem Multiple Choice a) If H 0 is false, then there is a chance equal to the p value that the value of the test statistic will be equal to or less than the calculated value b) If H 0 is true, then there is a chance equal to the p value that the value of the test statistic will be equal to or less than the calculated value c) If H 0 is true, then there is a chance equal to the p value that the value of the test statistic will be equal to or greater than the calculated value d) If H 0 is false, then there is a chance equal to the p value that the value of the test statistic will be equal to or greater than the calculated value Part (g) Sketch a picture of this situation Label and scale the horizontal axis, and shade the region(s) corresponding to the p value

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A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5% level to determine if

A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5% level to determine if the die is fair. The data below are the result of the 120 rolls. (Enter exact numbers as integers, fractions, or decimals.)

Be Careful with the rounding be sure to use all

Face Value Frequency Expected Frequency

1 14 ____________

2 32 ____________

3 15 _____________

4 14 _______________

5 31 _________

6 14 _____________

Part (a) Multiple Choice
State the null hypothesis.

a) The data fit the distribution for a fair six-sided die.

b) The data do not fit the distribution for a fair six-sided die.

Part (b) Multiple Choice
State the alternative hypothesis.

a) The data do not fit the distribution for a fair six-sided die.

b) The data fit the distribution for a fair six-sided die.

Part (c)
What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)
____________
Part (d) Multiple Choice
State the distribution to use for the test.

a) ?26

b) t₆

c) t₅

d) ?25

Part (e)
What is the test statistic? (Round your answer to two decimal places.)
__________
Part (f)
What is thep-value? (Round your answer to four decimal places.)

P=_________

Explain what thep-value means for this problem. Multiple Choice

a) IfH₀is false, then there is a chance equal to thep-value that the value of the test statistic will be equal to or less than the calculated value.

b) IfH₀is true, then there is a chance equal to thep-value that the value of the test statistic will be equal to or less than the calculated value.

c) IfH₀is true, then there is a chance equal to thep-value that the value of the test statistic will be equal to or greater than the calculated value.

d) IfH₀is false, then there is a chance equal to thep-value that the value of the test statistic will be equal to or greater than the calculated value.