Question 1207303
the mean of the sample = 98.366666667.
the standard deviation of the sample = 0.832165849.
the sample size is equal to 9.


t-score is indicated because you are using sample standard deviation.


critical t-score for 95% confidence interval with 8 degrees of freedom is equal to t = plus or minus 2.306004133.


t-score formula is t = (x - m) / s
t is the critical t-score
x is the critical raw score
m is the mean
s is the standard error.


standard error = standard deviation / sqrt(sample size) = 0.832165849 / sqrt(9) = .2773886163.


high side of the confidence interval t-score is 2.306004133 = (x - 98.366666667) / .2773886163.


solve for x to get x = 99.00632596.


low side of the confidence interval t-score is -2.306004133 = (x - 98.366666667) / .2773886163.


solve for x to get x = -2.306004133 * .2773886163 + 98.366666667 = 97.72700737.


your 95% confidence interval is from 97.72700737 to 99.00632596.


i used a descriptive statistic calculator to get the mean and standard deviation.
that calculator can be found at <a href = "https://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php" target = "_blank">https://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php</a>


enter your data as shown below, then hit "calculate" and the calculator does the rest.


<img src = "http://theo.x10hosting.com/2024/051801.jpg">


you'll need to run the calculator to see the results.


i also used a t-test confidence interval calculator to confirm the results.


here they are, from the calculator at <a href = "https://www.socscistatistics.com/confidenceinterval/default2.aspx" target = "_blank">https://www.socscistatistics.com/confidenceinterval/default2.aspx</a>


<img src = "http://theo.x10hosting.com/2024/051802.jpg">