the dollar value per sale that a small online candle shop makes is normally distributed with a population…
the dollar value per sale that a small online candle shop makes is normally distributed with a population standard deviation of 2.5 dollars and an unknown population mean. if a random sample of 25 transactions is taken and results in a sample mean of 9 dollars, find a 90% confidence interval for the population mean.\nuse the tool below to calculate your confidence interval. choose the correct confidence level, sample mean, population standard deviation, and sample size. then view the confidence interval indicated on the x-axis to find your answer. please note, youll need to use the sliders above the graph to change the x-axis markers. round your answers to 2 decimal places.
Answer
Explanation:
Step1: Identify critical z-value
For 90% confidence, the critical $z$-value is $z_{\alpha/2}=1.645$.
Step2: Calculate standard error
Standard error = $\frac{\sigma}{\sqrt{n}} = \frac{2.5}{\sqrt{25}}$ $\frac{2.5}{5}=0.5$
Step3: Compute margin of error
Margin of error = $z_{\alpha/2} \times \text{standard error} = 1.645 \times 0.5$ $1.645 \times 0.5=0.8225$
Step4: Find confidence interval
Lower bound: $\bar{x} - \text{margin of error} = 9 - 0.8225$ Upper bound: $\bar{x} + \text{margin of error} = 9 + 0.8225$ Round to 2 decimal places: Lower bound: $8.18$, Upper bound: $9.82$
Answer:
The 90% confidence interval for the population mean is (8.18, 9.82)