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The manager of a pharmacy wants to know if prescriptions arefilled uniformly over the 7 days of the week. The manager takes asimple random sample of 245 prescription receipts and finds thatthey are distributed as follows:

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Prescriptions	42	31	33	29	45	44	21

a. Which of the following is the appropriate null hypothesis forthis test?

1. H₀: p₁ =p₂ = p₃ =p₄ = p₅ =p₆ = p₇ = 1/7
2. H₀: p₁ =p₂ = p₃ =p₄ = p₅ = 5/7 andp₆ = p₇ = 2/7
3. H₀: p₁ = 0.17,p₂ = 0.13, p₃ = 0.13,p₄ = 0.12, p₅ = 0.18,p₆ = 0.18, p₇ = 0.09
4. None of the above

b. Under the null hypothesis of a uniform distribution ofprescriptions over the 7 days of the week, the expected count ofprescriptions for Monday is _____________ (show calculation).

c. Under the null hypothesis of a uniform distribution ofprescriptions over the 7 days of the week, the chi-squarecontribution for Monday is _________________ (showcalculation).

d. Under the null hypothesis of a uniform distribution ofprescriptions over the 7 days of the week, the degrees of freedomfor the chi-square test is _______________. (show calculation).

e. What is the chi-square statistic for testing this nullhypothesis of a uniform distribution of prescriptions over the 7days of the week (show calculation)?

a. 1/7

b. 3.5

c. 13.8

d. 24.5

f. What is the P-value for testing this null hypothesisof a uniform distribution of prescriptions over the 7 days of theweek? Specify the distribution used and all relevantparameters.

g. Using a significance level of 0.05, what is the appropriateconclusion for this test?

1. All 7 days of the week have different prescription rates.
2. There is significant evidence that prescriptions are notuniformly distributed over the 7 days of the week.
3. Weekdays and weekends have significantly different prescriptionrates.
4. The data are consistent with prescriptions being uniformlydistributed over the 7 days of the week.

h. What can we state about the chi-square test in thissituation?

a. The test is valid because the sample size is large.

b. The test is valid because the sample is random and theobserved counts are large enough.

c. The test is valid because the sample is random and theexpected counts are large enough.

d. The test is not valid because we do not know the truepopulation proportions.

i. Which of the following statements about a chi-squarehypothesis test is true?

1. When observed counts are far from expected counts, we haveevidence against H₀.
2. Large values of χ² indicate evidenceagainst H₀.
3. Expected counts are hypothetical, and do not have to be wholenumbers.
4. All of the above

j. Under which of the following conditions can a largeP- value arise?

1. H₀ is indeed true.
2. H₀ is not actually true, but too close tothe real population distribution for us to tell them apartstatistically.
3. H₀ is definitely not true, but the samplesize is too small or the variability is too great to reachsignificance.
4. All of the above