**Confidence Interval Construction Using the t-Distribution****Problem Statement:**Construct the indicated confidence interval for the population mean (μ) using the t-distribution. Assume the population is normally distributed.- Confidence level (c) = 0.95- Sample mean ($ \bar{x} $) = 12.6- Sample standard deviation (s) = 3.0- Sample size (n) = 10**Confidence Interval:**\[ (\_, \_) \]**Instructions:**Round to one decimal place as needed. **Understanding Confidence Intervals:**A confidence interval provides a range of values that is likely to contain the population mean (μ) with a certain level of confidence. When the population standard deviation is unknown and the sample size is small (typically n < 30), the t-distribution is more appropriate than the normal distribution for constructing the interval. Here, we use a 95% confidence level, which means we are 95% confident that the interval calculated from the sample data contains the true population mean. To calculate the confidence interval, you would generally follow these steps:1. Determine the t-score for your confidence level and degrees of freedom (df = n - 1).2. Calculate the standard error (SE) of the mean: SE = s / √n.3. Calculate the margin of error (ME): ME = t-score * SE.4. Determine the confidence interval: ( $ \bar{x} $ - ME, $ \bar{x} $ + ME ).**Note:** Provide actual values in place of placeholders after computation.

Name: **Confidence Interval Construction Using the t-Distribution****Proble
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: **Confidence Interval Construction Using the t-Distribution****Problem Statement:**Construct the indicated confidence interval for the population mean (μ) using the t-distribution. Assume the population is normally distributed.- Confidence level (c)

Answered: Construct the indicated confidence…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

100%

**Confidence Interval Construction Using the t-Distribution**

**Problem Statement:**

Construct the indicated confidence interval for the population mean (μ) using the t-distribution. Assume the population is normally distributed.

- Confidence level (c) = 0.95
- Sample mean ($ \bar{x} $) = 12.6
- Sample standard deviation (s) = 3.0
- Sample size (n) = 10

**Confidence Interval:**

\[ (\_, \_) \]

**Instructions:**

Round to one decimal place as needed.

**Understanding Confidence Intervals:**

A confidence interval provides a range of values that is likely to contain the population mean (μ) with a certain level of confidence. When the population standard deviation is unknown and the sample size is small (typically n < 30), the t-distribution is more appropriate than the normal distribution for constructing the interval. Here, we use a 95% confidence level, which means we are 95% confident that the interval calculated from the sample data contains the true population mean.

To calculate the confidence interval, you would generally follow these steps:

1. Determine the t-score for your confidence level and degrees of freedom (df = n - 1).
2. Calculate the standard error (SE) of the mean: SE = s / √n.
3. Calculate the margin of error (ME): ME = t-score * SE.
4. Determine the confidence interval: ( $ \bar{x} $ - ME, $ \bar{x} $ + ME ).

**Note:** Provide actual values in place of placeholders after computation.

Expert Solution

Step 1

$\mathbf{Solution}$

$\mathrm{\mathbf{given}:}$

$\mathrm{Confidence\;level\;(C)=0.95\;or\;95\%}$

$\mathrm{Sample\;mean\;(\bar x)=12.6}$

$\mathrm{Sample\;standard\;deviation\;(s)=3.0}$

$\mathrm{Sample\;size\;(n)=10}$

Since population standard deviation is unknown, Use t-distribution to find t-critical value.

Find the t-critical value:

$\mathbf{Degrees\;of\;freedom\;(df)}=n-1=10-1=\mathbf{9}$

Refer t-distribution table and look for t value corresponding to degrees of freedom=9 & confidence level of 95%.

Therefore,

$\mathbf{t_{\frac{\alpha }{2}}=2.262 }$

Step by step

Solved in 2 steps with 15 images

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions