After getting trounced by your little brother in achildren's game, you suspect the die he gave you to roll may be unfair. Tocheck, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on thedie's fairness?

Face 1 2 3 4 5 6

Count 15 15 6 14 6 4

a) If the die isfair, how many times would you expect each face toshow?

__.

b) To see if these results areunusual, will you testgoodness-of-fit, homogeneity, orindependence?

A. Goodness-of-fit

B. Homogeneity

C. Independence

c) State your hypotheses.

A. H0: The die is unfair. HA: The die is fair.

B. H0: The die is fair. HA: The die produces outcomes that are greater than the expected value.

C. H0: The die is fair. HA: The die produces outcomes that are less than the expected value.

D. H0: The die is fair. HA: The die is unfair.

d) Check the conditions. Is the counted data conditionmet?

a) No

b) Yes

Is the randomization conditionmet?

a) Yes

b) No

Is the expected cell frequency conditionmet?

a) No

b) Yes

e) How many degrees of freedom arethere?

__.

f) Find 2 and theP-value. (Round to four decimal places asneeded.)

2= __.

Find theP-value.

a) 0.0801

b) 0.0199

c) 0.9801

g) State your conclusion. Assume that 0.05 is a reasonable significance level.

A. Failtoreject the null hypothesis. There isnot sufficient evidence to support the claim.

B. Reject the null hypothesis. There is not sufficient evidence to support the claim.

C. Failtoreject the null hypothesis. There is sufficient evidence to support the claim.

D. Reject the null hypothesis. There issufficient evidence to support the claim.

Please show all work. thank you!