The average daily volume of a computer stock in 2011 was μ = 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 27.6 million shares, with a standard deviation of s = 11.4 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below. (a) State the hypotheses for the test. Hoi H = 35.1 million shares H₁: H # 35.1 million shares (b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018. million shares. With 95% confidence, the mean stock volume in 2018 is between million shares and (Round to three decimal places as needed.)
The average daily volume of a computer stock in 2011 was μ = 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 27.6 million shares, with a standard deviation of s = 11.4 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below. (a) State the hypotheses for the test. Hoi H = 35.1 million shares H₁: H # 35.1 million shares (b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018. million shares. With 95% confidence, the mean stock volume in 2018 is between million shares and (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![**Average Daily Stock Volume Analysis**
**Introduction:**
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 27.6 million shares, with a standard deviation of \(s\) = 11.4 million shares. We will test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below.
**(a) State the hypotheses for the test.**
\[
\begin{aligned}
H_0: \mu &= 35.1 \text{ million shares} \\
H_1: \mu &\neq 35.1 \text{ million shares}
\end{aligned}
\]
**(b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018.**
With 95% confidence, the mean stock volume in 2018 is between \(\boxed{ }\) million shares and \(\boxed{ }\) million shares. (Round to three decimal places as needed.)
**Explanation:**
To construct the 95% confidence interval, we will use the formula for the confidence interval of the mean when the population standard deviation is unknown:
\[
\bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right)
\]
Where:
- \(\bar{x}\) is the sample mean (27.6 million shares),
- \(s\) is the sample standard deviation (11.4 million shares),
- \(n\) is the sample size (30),
- \(t\) is the critical value from the t-distribution for 95% confidence with \(n - 1\) degrees of freedom (29 degrees of freedom).
1. Calculate the sample standard error:
\[
\frac{s}{\sqrt{n}} = \frac{11.4}{\sqrt{30}} \approx 2.081
\]
2. Determine the t-critical value for 95% confidence and 29 degrees of freedom. (Using a t-table or calculator, the value is approximately 2.045).
3. Calculate the margin of error:
\[
t \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbaaf3a5-97a4-44d4-82b4-c685cbb2fa1a%2F101e4652-ecae-4990-97a4-be0133210854%2Fgz2jkyu_processed.png&w=3840&q=75)
Transcribed Image Text:**Average Daily Stock Volume Analysis**
**Introduction:**
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 27.6 million shares, with a standard deviation of \(s\) = 11.4 million shares. We will test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below.
**(a) State the hypotheses for the test.**
\[
\begin{aligned}
H_0: \mu &= 35.1 \text{ million shares} \\
H_1: \mu &\neq 35.1 \text{ million shares}
\end{aligned}
\]
**(b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018.**
With 95% confidence, the mean stock volume in 2018 is between \(\boxed{ }\) million shares and \(\boxed{ }\) million shares. (Round to three decimal places as needed.)
**Explanation:**
To construct the 95% confidence interval, we will use the formula for the confidence interval of the mean when the population standard deviation is unknown:
\[
\bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right)
\]
Where:
- \(\bar{x}\) is the sample mean (27.6 million shares),
- \(s\) is the sample standard deviation (11.4 million shares),
- \(n\) is the sample size (30),
- \(t\) is the critical value from the t-distribution for 95% confidence with \(n - 1\) degrees of freedom (29 degrees of freedom).
1. Calculate the sample standard error:
\[
\frac{s}{\sqrt{n}} = \frac{11.4}{\sqrt{30}} \approx 2.081
\]
2. Determine the t-critical value for 95% confidence and 29 degrees of freedom. (Using a t-table or calculator, the value is approximately 2.045).
3. Calculate the margin of error:
\[
t \times
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