Question

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

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

Which of the following is the appropriate null hypothesis for this test?

1. H₀: p₁= p₂= p₃= p₄= p₅= p₆= p₇= 1/7
2. H₀: p₁= p₂= p₃= p₄= p₅= 5/7 and p₆= 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

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

Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the chi-square contribution for Monday is _________________ (show calculation).

Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the degrees of freedom for the chi-square test is _______________.

Answer 1

Null hypothesis:

H₀: p₁= p₂= p₃= p₄= p₅= p₆= p₇= 1/7

Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the expected count of prescriptions for Monday is =np=245*1/7 =35

Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the chi-square contribution for Monday is =(O-E)^2/E =(42-35)^2/35 =1.4

Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the degrees of freedom for the chi-square test is =categories -1 =7-1 =6