**Educational Text and Explanation of Graphs**You have taken a random sample of size \( n = 19 \) from a normal population that has a population mean of \( \mu = 50 \) and a population standard deviation of \( \sigma = 15 \). Your sample, which is Sample 1 in the table below, has a mean of \( \bar{x} = 45.3 \).### Instructions:**(a)** Based on Sample 1, graph the 75% and 90% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidence interval, and use 1.645 for the critical value for the 90% confidence interval.- Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.- For the points (\(\color{red} \bullet\) and \(\color{blue} \bullet\)), enter the population mean, \(\mu = 50\).**Graphical Explanation:**1. **75% Confidence Interval:** - A line is shown with markers from approximately 37.0 to 66.0, centering around a mean value for the sample (\(45.3\)), with a marker at 51.5 indicating the interval center.2. **90% Confidence Interval:** - Similarly, a line shows values from approximately 37.0 to 66.0, with a marker at 51.5 for the interval center.**(b)** Press the "Generate Samples" button to simulate taking 19 more samples of size \( n = 19 \) from the population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.**Table and Additional Graphs:**The table shows sample means (\(S1\) to \(S20\)) and placeholders for confidence interval limits. The columns indicate:- Each sample's mean- The lower and upper limits for both 75% and 90% confidence intervals**Graphical Explanation:**- The left side shows a vertical array of the 75% confidence intervals for each sample.- The right side shows a vertical array of the 90% confidence intervals.The graphs demonstrate how each sample’s confidence interval is calculated and illustrates the distribution of sample means around the population mean (\( \ (c) Notice that for \( \frac{16}{20} = 80\% \) of the samples, the 90% confidence interval contains the population mean. Choose the correct statement.- ○ When constructing 90% confidence intervals for 20 samples of the same size from the population, at most 90% of the samples will contain the population mean.- ○ When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% of the samples must contain the population mean. There must have been an error with the way our samples were chosen.- ○ When constructing 90% confidence intervals for 20 samples of the same size from the population, the percentage of the samples that contain the population mean should be close to 90%, but it may not be exactly 90%.(d) Choose ALL that are true.- □ The 75% confidence interval for Sample 15 indicates that 75% of the Sample 15 data values are between 44.4 and 52.4.- □ From the 90% confidence interval for Sample 15, we cannot say that there is a 90% probability that the population mean is between 42.7 and 54.1.- □ If there were a Sample 21 of size \( n = 38 \) taken from the same population as Sample 15, then the 90% confidence interval for Sample 21 would be narrower than the 90% confidence interval for Sample 15.- □ The 75% confidence interval for Sample 15 is narrower than the 90% confidence interval for Sample 15. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval.- □ None of the choices above are true.

Here we have give that,sample size = n = 19Population Mean = µ = 50Population Standard Deviation = σ…

Answered: You have taken a random sample of size…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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QUESTION 1 The U.S. Mint produces approximately 13 billion pennies a year. A random sample (n-800) of pennies were collected and their minted years were recorded. The output, histogram, box-plot, and QQ plot for the distribution of the years of production for the pennies can be found on the attached document. PenniesNormalitylnformation 200405.pdf The mean is only slightly less than the is left skewed. which suggests the distribution 1. histogram v This is within the acceptable range (between -1 and +1). Interquartile range 2. The is also between the acceptable range of -3 and +3. 3. kurtosis v The has only one mode and the tails are approximately equal length. 4. longer 5. median The box and whisker plot shows the median is approximately in the center of the 6. Normal v The left whisker is slightly than the right whisker. 7. QQ Plot v The raw scores hug the theoretical line on the 8. shorter Therefore, there is enough evidence to assume that the data can be considered 9. skewness 10.…
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Question 5, 8.3.49
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Imagine that a study of memory and aging finds that younger participants correctly recall 55% of studied words, older participants correctly recall 42% of studied words, and the size of this effect is Cohen's d = 0.49. This effect size indicates that the memory performance of: Question 10 options: younger participants is approximately half a standard deviation below that of older participants. older participants is approximately half a standard deviation below that of younger participants. younger participants is significantly lower than that of older participants. older participants is approximately 4 standard deviations below that of younger participants.
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