a. Create a histogram OR boxplot by year for the number of patients in the emergency room. What do you notice between the two years? | ||||||||||

b. You want to answer the question: Is there a difference in the average number of patients being seen in the emergency room between 2015 and 2016? | ||||||||||

Why would an independent samples t-test be most appropriate? | ||||||||||

Answered Same DaySep 24, 2021

Q1

# of Patients (25 pts) 1. You want to go to your boss and ask for additional staff in your emergency room. You have noticed an increase in patients in the ER since the previous year.

Year You collect data by month for the two years to compare. Assume that the number of patients are normally distributed.

Month 2015 2016 Histogram

1 4825 5262

2 4752 5435 a. Create a histogram OR boxplot by year for the number of patients in the emergency room. What do you notice between the two years?

3 4948 5481

4 5041 6081 Histogram is given on right side

5 5300 5936 we observe that there is an increase from 2015 to 2016 in general.

6 5232 5627

7 5151 5856

8 5585 5763 b. You want to answer the question: Is there a difference in the average number of patients being seen in the emergency room between 2015 and 2016?

9 5520 5924 Why would an independent samples t-test be most appropriate?

10 5136 5787 1) Because this is comparison of statistical differences between the means of two groups

11 5077 5474 2) Because one variable is numerical and other is categorical

12 5300 5699 3) Random sampling is done

4) There is homogenity of variances

5) Normality is assumed

6) Outliers are not present.

c. State your null and alternative hypothesis in words and symbols for an independent samples t-test.

Symbols H0: Mean 2015 = Mean 2016

Ha: Mean 2015 < Mean 2016

Words H0: the average number of emergency patients in the year 2016 is the same as that in 2015

Ha: the average number of emergency patients in the year 2016 is more than that in 2015

d. You set your level of significance at alpha = 0.05 and determine your t-critical value of 2.074 since you are decided to conduct a t-test.

What is your decision rule (state when would you reject the null hypothesis and when you would fail to reject the null hypothesis)

We find test statistic for mean difference. If the test statistic t >2.074 we reject null hypothesis and accept there is an incrase in no o fpatients

in 2016.

e. Using Data Analysis in Excel, you obtain the following table. Make a conclusion. Your conclusion should have two parts.

1) Do you reject or fail to reject the null hypothesis based on your decision rule?

We find p value is less than 0.05

Hence reject null hypothesis.

2) Answer the question (relate your conclusion back to the question asked) based on your decision.

There is statistical evidence at 95% level to show that the number of emergency patients increased

in 2016 from 2015

t-Test: Two-Sample Assuming Unequal Variances

2016 2015

Mean 5693.75 5155.5833333333

Variance 59352.2045454545 63610.446969697

Observations 12 12

Hypothesized Mean Difference 0

df 22

t Stat 5.3164386655

p-value--> P(T<=t) two-tail 0.0000245703

tcv --> t Critical two-tail 2.0738730679

0 1 2 3 4 5 6 7 8 9 10 11 12 2015 4825 4752 4948 5041 5300 5232 5151 5585 5520 5136 5077 5300 2016 5262 5435 5481 6081 5936 5627 5856 5763 5924 5787 5474 5699

Q2

2. You think that there may be differences in the demand for emergency room services depending on the day of the week. (5 pts)

In order to co

ectly staff your emergency room, you decide to look at demand by day of the week.

You gather the number of patients seen in the ER by day of week.

Question: Is there a difference in the average number of patients being seen in the emergency room by day of week?

a. What is the most appropriate test to statistically test this hypothesis? Why?

If we want to check for a week containing 7 days, chi square test for goodness of fit is the most appropriate test

b. State...

# of Patients (25 pts) 1. You want to go to your boss and ask for additional staff in your emergency room. You have noticed an increase in patients in the ER since the previous year.

Year You collect data by month for the two years to compare. Assume that the number of patients are normally distributed.

Month 2015 2016 Histogram

1 4825 5262

2 4752 5435 a. Create a histogram OR boxplot by year for the number of patients in the emergency room. What do you notice between the two years?

3 4948 5481

4 5041 6081 Histogram is given on right side

5 5300 5936 we observe that there is an increase from 2015 to 2016 in general.

6 5232 5627

7 5151 5856

8 5585 5763 b. You want to answer the question: Is there a difference in the average number of patients being seen in the emergency room between 2015 and 2016?

9 5520 5924 Why would an independent samples t-test be most appropriate?

10 5136 5787 1) Because this is comparison of statistical differences between the means of two groups

11 5077 5474 2) Because one variable is numerical and other is categorical

12 5300 5699 3) Random sampling is done

4) There is homogenity of variances

5) Normality is assumed

6) Outliers are not present.

c. State your null and alternative hypothesis in words and symbols for an independent samples t-test.

Symbols H0: Mean 2015 = Mean 2016

Ha: Mean 2015 < Mean 2016

Words H0: the average number of emergency patients in the year 2016 is the same as that in 2015

Ha: the average number of emergency patients in the year 2016 is more than that in 2015

d. You set your level of significance at alpha = 0.05 and determine your t-critical value of 2.074 since you are decided to conduct a t-test.

What is your decision rule (state when would you reject the null hypothesis and when you would fail to reject the null hypothesis)

We find test statistic for mean difference. If the test statistic t >2.074 we reject null hypothesis and accept there is an incrase in no o fpatients

in 2016.

e. Using Data Analysis in Excel, you obtain the following table. Make a conclusion. Your conclusion should have two parts.

1) Do you reject or fail to reject the null hypothesis based on your decision rule?

We find p value is less than 0.05

Hence reject null hypothesis.

2) Answer the question (relate your conclusion back to the question asked) based on your decision.

There is statistical evidence at 95% level to show that the number of emergency patients increased

in 2016 from 2015

t-Test: Two-Sample Assuming Unequal Variances

2016 2015

Mean 5693.75 5155.5833333333

Variance 59352.2045454545 63610.446969697

Observations 12 12

Hypothesized Mean Difference 0

df 22

t Stat 5.3164386655

p-value--> P(T<=t) two-tail 0.0000245703

tcv --> t Critical two-tail 2.0738730679

0 1 2 3 4 5 6 7 8 9 10 11 12 2015 4825 4752 4948 5041 5300 5232 5151 5585 5520 5136 5077 5300 2016 5262 5435 5481 6081 5936 5627 5856 5763 5924 5787 5474 5699

Q2

2. You think that there may be differences in the demand for emergency room services depending on the day of the week. (5 pts)

In order to co

ectly staff your emergency room, you decide to look at demand by day of the week.

You gather the number of patients seen in the ER by day of week.

Question: Is there a difference in the average number of patients being seen in the emergency room by day of week?

a. What is the most appropriate test to statistically test this hypothesis? Why?

If we want to check for a week containing 7 days, chi square test for goodness of fit is the most appropriate test

b. State...

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