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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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