A food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed their contents.If the sample mean is 10.0 and the sample standard deviation is 0.15, find the 95% confidence interval of the true mean.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (± .025) and its Z score.
95% = mean ± Z SEm
SEm = SD/√n
To find the 95% confidence interval of the true mean, you can use the following formula:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √n)
In this case, the sample mean is 10.0, the sample standard deviation is 0.15, and the sample size is 15.
Step 1: Determine the Critical Value
The critical value is found by looking up the z-score for the desired confidence level. For a 95% confidence level, the critical value is approximately 1.96 (obtained from the z-table or using a calculator).
Step 2: Calculate the Standard Error (Standard Deviation / √n)
Standard Error = 0.15 / √15
Step 3: Calculate the Confidence Interval
Confidence Interval = 10.0 ± (1.96) * (0.15 / √15)
Now, let's calculate the values.
Calculating the Standard Error:
Standard Error = 0.15 / √15
Standard Error ≈ 0.0387
Calculating the Confidence Interval:
Confidence Interval = 10.0 ± (1.96) * (0.0387)
Confidence Interval ≈ 10.0 ± 0.0758
Therefore, the 95% confidence interval of the true mean is approximately (9.9242, 10.0758).