During one week in a rural hospital, 9 new cases of COVID-19 were admitted. Standard procedure is to take the patient’s temperature when tested. The New York State Health officials claim that the mean temperature of a person testing positive for the virus is 102 degrees fahrenheit. This is very conscientious small hospital; they do their own tests and find the following results for those 9 patients: Temperatures (Degrees fahrenheit): 100, 99, 102, 101, 99, 101, 99, 98, 100. Can we reject the NYS Health data based on our own findings? Please calculate the test statistic and pvalue. What can be concluded? Support your answer. Please calculate the 95% confidence interval Interpret the interval. What can be concluded? Support your answer.
During one week in a rural hospital, 9 new cases of COVID-19 were admitted. Standard procedure is to take the patient’s temperature when tested. The New York State Health officials claim that the mean temperature of a person testing positive for the virus is 102 degrees fahrenheit. This is very conscientious small hospital; they do their own tests and find the following results for those 9 patients:
Temperatures (Degrees fahrenheit): 100, 99, 102, 101, 99, 101, 99, 98, 100.
Can we reject the NYS Health data based on our own findings?
- Please calculate the test statistic and pvalue.
- What can be concluded? Support your answer.
- Please calculate the 95% confidence interval
- Interpret the interval.
- What can be concluded? Support your answer.
State the hypotheses.
That is, the mean temperature of a person testing positive for the virus is 102 degrees Fahrenheit
That is, the mean temperature of a person testing positive for the virus is not 102 degrees Fahrenheit.
Decision rule:
Obtain the value of the test statistic.
The value of the test statistic is obtained below:
Use EXCEL Procedure for mean and standard deviation for the given samples.
Follow the instruction to obtain the values of mean and SD:
- Open EXCEL
- Go to Data>Data Analysis.
- Choose Descriptive Statistics.
- Enter the input range as $A$1:$A$10.
- Check the Labels in the first row.
- Check the option Summary statistics
- Click OK.
EXCEL output:
From the EXCEL output, the value of mean is 99.8889 and the standard deviation is 1.2693.
The required value is,
Thus, the value of the test statistic is –4.99
Obtain the degrees of freedom.
The degrees of freedom is obtained below:
Use EXCEL Procedure for finding the P-value.
Follow the instruction to obtain the P-value:
- Open EXCEL
- Go to Formula bar.
- In formula bar enter the function as“=TDIST”
- Enter the test statistic value as ABS( –4.99).
- Enter the degrees of freedom as 8
- Enter the tail as 2.
- Click enter
EXCEL output:
From the EXCEL output, the P-value is 0.0011
Thus, the P-value is 0.0011.
The conclusion is obtained as shown below:
Conclusion:
Use the level of significance is 0.05.
The p-value is less than level of significance.
By rejection rule, reject the null hypothesis.
That is, the mean temperature of a person testing positive for the virus is not 102 degrees Fahrenheit.
Yes, we can reject the NYS Health data based on our own findings.
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