The average daily volume of a computer stock in 2011 was $\mu=35.1$ million shares, according to a reliable source. A stock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 30 trading days in 2018 , he finds the sample mean to be 29.8 million shares, with a standard deviation of $s=15.1$ million shares. Test the hypotheses by constructing a 95\% confidence interval. Complete parts (a) through (c) below
(b) Construct a 95\% contıdence ınterval about the sample mean of stocks traded in 2018.
With $95 \%$ confidence, the mean stock volume in 2018 is between million shares and million shares. (Round to three decimal places as needed.)
Answer
Final Answer: With 95% confidence, the mean stock volume in 2018 is between \(\boxed{24.397}\) million shares and \(\boxed{35.203}\) million shares.
Step 1 ：Given that the sample mean (\(\bar{x}\)) is 29.8 million shares, the z-score (z) is 1.96, the sample standard deviation (s) is 15.1 million shares, and the sample size (n) is 30.
Step 2 ：We can use the formula for a confidence interval, which is \(\bar{x} \pm z \frac{s}{\sqrt{n}}\).
Step 3 ：Substitute the given values into the formula to calculate the margin of error: \(1.96 \times \frac{15.1}{\sqrt{30}}\), which is approximately 5.403.
Step 4 ：Subtract the margin of error from the sample mean to get the lower bound of the confidence interval: \(29.8 - 5.403\), which is approximately 24.397.
Step 5 ：Add the margin of error to the sample mean to get the upper bound of the confidence interval: \(29.8 + 5.403\), which is approximately 35.203.
Step 6 ：Final Answer: With 95% confidence, the mean stock volume in 2018 is between \(\boxed{24.397}\) million shares and \(\boxed{35.203}\) million shares.
