Answer :
Answer:
The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).
Step-by-step explanation:
The question is incomplete:
"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."
We start by calculating the mean of the sample:
[tex]M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is know and is σ=24.
The sample mean is M=146.
The sample size is N=9.
As σ is known, the standard error of the mean (σM) is calculated as: [tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{24}{\sqrt{9}}=\dfrac{24}{3}=8[/tex]
The z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_M=1.96 \cdot 8=15.68[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 146-15.68=130.32\\\\UL=M+t \cdot s_M = 146+15.68=161.68[/tex]
The 95% confidence interval for the population mean is (130.32, 161.68).