Here are the Degree of Reading Power (DRP) scores for a random sample of 10 third grade students in the Albany City school district: 31, 27, 38, 34, 42, 28, 26, 43, 46, 27 You wonder whether the mean score of this sample is greater than the population mean of all third grade students in the Albany City school district, which is 30. Suppose scores on the DRP are known to be normally distributed with a population standard deviation of 11. Step 1)Population 1 (Sample):Population 2: Null Hypothesis (H0):Research Hypothesis (H1): Step 2) Determine the characteristics of the comparison distribution.Sample Mean = M = _________Mean of the population = μ = ________Population standard deviation = = _________Standard deviation of distribution of means = = __________ Step 3) Determine the cutoff score on the z distribution (use a 0.05 p value). Cut-off score = _________ Step 4) Determine your sample’s z score. z = ___________ Step 5) Decide whether or not to reject null hypothesis. What conclusion can you make? Is the mean DRP score of Albany third graders greater than 30?

Answered: Step 1) Population 1 (Sample):…

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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Here are the Degree of Reading Power (DRP) scores for a random sample of 10 third grade students in the Albany City school district:

31, 27, 38, 34, 42, 28, 26, 43, 46, 27

You wonder whether the mean score of this sample is greater than the population mean of all third grade students in the Albany City school district, which is 30. Suppose scores on the DRP are known to be normally distributed with a population standard deviation of 11.

Step 1)

Population 1 (Sample):
Population 2:

Null Hypothesis (H₀):
Research Hypothesis (H₁):

Step 2) Determine the characteristics of the comparison distribution.

Sample Mean = M = _________
Mean of the population = μ = ________
Population standard deviation = = _________
Standard deviation of distribution of means = = __________

Step 3) Determine the cutoff score on the z distribution (use a 0.05 p value).

Cut-off score = _________

Step 4) Determine your sample’s z score.

z = _{___________}

Step 5) Decide whether or not to reject null hypothesis. What conclusion can you make? Is the mean DRP score of Albany third graders greater than 30?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Step 1:

Let $μ$ denotes the population mean.

The claim of the test is mean score of this sample is greater than the population mean of all third grade students in the Albany City school district, which is 30. The hypothesis is,

Null hypothesis:

$H_{0} : μ \leq 30$

Alternative hypothesis:

$H_{1} : μ > 30$

Step 2:

The sample mean is,

$\begin{array}{rcl} M & = & \frac{\sum_{i} X}{n} \\ = & \frac{31 + 27 + 38 + 34 + 42 + 28 + 26 + 43 + 46 + 27}{10} \\ = & \frac{342}{10} \\ = & 34.2 \end{array}$

Thus, the sample mean is 34.2.

The population mean $(μ)$ is 30, population standard deviation $(σ)$ is 11.

The standard deviation of distributions of means is,

$\begin{array}{rcl} σ_{\bar{x}} & = & \frac{σ}{\sqrt{n}} \\ = & \frac{11}{\sqrt{10}} \\ = & 3.4785 \end{array}$

Thus, the standard deviation of distributions of means is 3.4785.

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