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# 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...

 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?

## Solution

Rajeswari answered on Sep 25 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.
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...
SOLUTION.PDF