This Venn diagram shows sports played by 10 students.
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Answer:
The 86% confidence interval for the population mean is (19.982, 23.018).
As we are using a sample to make an inference about the population mean, we use a confidence interval with a certain degree of confidence.
We are 86% confident that the true mean ACT scores is between 19.982 and 23.018.
Step-by-step explanation:
We have the information:
Sample size n= 20
Mean M=21.5
STD s=5.7
Min = 15
Max = 26
Population STD σ=4.6
Confidence level = 86%
We have to calculate a 86% confidence interval for the mean.
The population standard deviation is know and is σ=4.6.
The sample mean is M=21.5.
The sample size is N=20.
As σ is known, the standard error of the mean (σM) is calculated as:
The t-value for a 86% confidence interval is z=1.476.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 86% confidence interval for the population mean is (19.982, 23.018).
As we are using a sample to make an inference about the population mean, we use a confidence interval with a certain degree of confidence.
We are 86% confident that the true mean ACT scores is between 19.98 and 23.02.