A1.3
C I FOR A POPULATION MEAN and the STANDARD DEVIATION IS UNKNOWN
The question:
An SRS of 75 females attending an all-female college was taken to study the amount for time they studied per week. Results indicated a mean of 73 minutes with a standard deviation of 21 minutes. Find the 95% confidence interval of the mean for all females spent studying. Interpret this interval in words.
The question stem: What are they asking you to determine?
Find the 95% confidence interval of the mean for all females spent studying. Interpret the interval in words.
What are you given?
An SRS of 75 females attending an all-female college was taken to study the amount of time they studied per week. Results indicated a mean of 73 minutes with a standard deviation of 21 minutes. Find the 95% confidence interval of the mean for all females spent studying. Interpret this interval in words.
Identify your variables:
*simple random sample (SRS)
* = the sample mean = 73 minutes
*n = 75 females
* = is unknown but we know the sample standard deviation, s.
* s = 21 minutes
*95% confidence in the results, which means critical value is 1.96
Note: Because we do not have the population standard deviation we will have to use the t- interval function. If the case were also that we lacked a large enough sample hence n<30, we would also have to use the t-interval.
The formula: for a One Sample T Interval (TInterval)
Question type: T-interval, Note: You will use the Interval functions in the calculator when you are preparing a confidence interval. You will also need to use the t-table to locate the critical value using the degrees of freedom and the alpha value.
Calculation: Using the T1-83: T Interval
Select STAT -> TEST -> T Interval. Note select stats note data in this case
You will need , calculate
This gives you a confidence interval of (68.17 min, 77.83 min)
Interpretation:
We are 95% confident that the true mean time relating to amount of time (in minutes) studying falls within the interval (68.17. 77.83)
