Question

In: Statistics and Probability

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7...

  1. 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
  1. 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).
  1. 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).
  1. 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 _______________.
  1. What is the chi-square statistic for testing this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week (show calculation)?

  1. 1/7
  2. 3.5
  3. 13.8
  4. 24.5

            245/7 = 35

  1. What is the P-value for testing this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week? Specify the distribution used and all relevant parameters.

  1. Using a significance level of 0.05, what is the appropriate conclusion for this test?
  1. All 7 days of the week have different prescription rates.
  2. There is significant evidence that prescriptions are not uniformly distributed over the 7 days of the week.
  3. Weekdays and weekends have significantly different prescription rates.
  4. The data are consistent with prescriptions being uniformly distributed over the 7 days of the week.
  1. What can we state about the chi-square test in this situation?
  1. The test is valid because the sample size is large.
  2. The test is valid because the sample is random and the observed counts are large enough.
  3. The test is valid because the sample is random and the expected counts are large enough.
  4. The test is not valid because we do not know the true population proportions.

Solutions

Expert Solution

Correct answer: Option (A) 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 245/7 = 35

since sum of all observed frequencies 42+31+33+29+45+44+21 = 245

Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the chi-square contribution for Monday is (42-35)^2 / 35 = 1.40

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 7-1 = 6

From the given data

Observed Expected
Day Freq (Oi) Freq Ei (Oi-Ei)^2 /Ei
Monday 42 35.00 1.4000
Tuesday 31 35.00 0.4571
Wednesday 33 35.00 0.1143
Thursday 29 35.00 1.0286
Friday 45 35.00 2.8571
Saturday 44 35.00 2.3143
Sunday 21 35.00 5.6000
Total: 245 245 13.7714

the chi-square statistic for testing this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week is 13.7714

P-Value: 0.0323

since P-value < alpha 0.05 so we reject H0

thus we conclude that Option (B) There is significant evidence that prescriptions are not uniformly distributed over the 7 days of the week.

Correct answer: Option (C) The test is valid because the sample is random and the expected counts are large enough.


Related Solutions

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7...
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? H0: p1 = p2 = p3 = p4 = p5 = p6 =...
The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7...
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 What is the chi-square statistic for testing this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week? ********************PLEASE SHOW...
The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7...
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 a. Which of the following is the appropriate null hypothesis for this test? H0: p1 = p2 = p3 = p4 = p5 = p6...
Exercise 1.6 Consider the following process at a pharmacy. Customers drop off their prescriptions either in...
Exercise 1.6 Consider the following process at a pharmacy. Customers drop off their prescriptions either in the drive-through counter or in the front counter of the pharmacy. Customers can request that their prescription be filled immediately. In this case, they have to wait between 15 minutes and one hour depending on the current workload. Most customers are not willing to wait that long, so they opt to nominate a pickup time at a later point during the day. Generally, customers...
Consider the following process at a pharmacy. Customers drop off their prescriptions either in the drive-through...
Consider the following process at a pharmacy. Customers drop off their prescriptions either in the drive-through counter or in the front counter of the pharmacy. Customers can request that their prescription be filled immediately. In this case, they have to wait between 15 minutes and one hour depending on the current workload. Most customers are not willing to wait that long, so they opt to nominate a pickup time at a later point during the day. Generally, customers drop their...
2. The manager of a restaurant wants to know if there is a correlation between the...
2. The manager of a restaurant wants to know if there is a correlation between the amount of a customer’s bill and the percent that they tip. In other words, as people spend more money do they tend to tip at different rates? With data from a random sample of 157 bills, he used StatKey to construct a 95% bootstrap confidence interval of [0.018, 0.292] for r. [24 points] A. What if the manager wanted to do a hypothesis test...
A branch manager has 4 inside sales employees. The manager wants to know if there is...
A branch manager has 4 inside sales employees. The manager wants to know if there is any difference between these employees in terms of average time to enter an order into the system. You are tasked to evaluate the collected data and prepare a report regarding your findings. Order Number Employee I Employee II Employee III Employee IV Time to Enter (in minutes) 1 5 12 8 10 2 7 12 11 9 3 9 2 7 5 4 6...
A fund manager wants to know if it is equally likely that the Nasdaq Average will...
A fund manager wants to know if it is equally likely that the Nasdaq Average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Nasdaq Average goes up. Day of the Week Observed Monday 192 Tuesday 189 Wednesday 202 Thursday 199 Friday 218 For the goodness-of-fit test, the null and alternative hypotheses are ________. H0: p1 = p2 = p3 = p4 = 1/4,...
A food services manager for a baseball park wants to know if there is a relationship...
A food services manager for a baseball park wants to know if there is a relationship between gender (male or female) and the preferred condiment on a hot dog. The following table summarizes the results. Test the hypothesis with a significance level of 10%. Condiment Gender Ketchup Mustard Relish Total Male 15 23 10 48 Female 25 19 8 52 Total 40 42 18 100 A food services manager for a baseball park wants to know if there is a...
Scenario You are a manager at a retail pharmacy outlet called One Pharmacy. Your store is...
Scenario You are a manager at a retail pharmacy outlet called One Pharmacy. Your store is in a very socially and culturally diverse suburb. Sometimes your staff members complain that the customers they serve are rude, unreasonable or difficult to understand. You realise your customer service systems may need to be reviewed and updated to best support your staff in serving the needs of your customers 1.1)   Customer service standards should ensure all customers are treated with respect, and staff members...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT