A random sample of77eighth grade students' scores on a national mathematics assessment test has a mean score of278.This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than270.Assume that the population standard deviation is35.Atα=0.11,is there enough evidence to support the administrator's claim? Complete parts (a) through (e).(a) Write the claim mathematically and identifyH0andHa.Choose the correct answer below. A.H0:μ=270Ha:μ>270(claim) B.H0:μ=270(claim)Ha:μ>270 C.H0:μ≤270Ha:μ>270(claim) D.H0:μ≥270(claim)Ha:μ<270 E.H0:μ≤270(claim)Ha:μ>270 F.H0:μ<270Ha:μ≥270(claim) (b) Find the standardized test statistic z, and its corresponding area. z=(Round to two decimal places as needed.) Find the P-value. P-value=(Round to three decimal places as needed.) (C)Decide whether to reject or fail to reject the null hypothesis. 1.Reject H0 2.Fail to reject H0 Interpret your decision in the context of the original claim. At the11%significance level, there▼1.is2.is notenough evidence to▼1.support2.rejectthe administrator's claim that the mean score for the state's eighth graders on the exam is more than270.

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Description: A random sample of77eighth grade students' scores on a national mathematics assessment test has a mean score of278.This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is m

Null and alternate hypotheses: The investigator is interested to test whether the mean score for the…

Answered: A random sample of 77 eighth grade…

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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A random sample of

eighth grade students' scores on a national mathematics assessment test has a mean score of

278.

This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than

270.

Assume that the population standard deviation is

35.

α=0.11,

is there enough evidence to support the administrator's claim? Complete parts (a) through (e).

(a) Write the claim mathematically and identify

and

Ha.

Choose the correct answer below.

H0:μ=270

Ha:μ>270(claim)

H0:μ=270(claim)

Ha:μ>270

H0:μ≤270

Ha:μ>270(claim)

H0:μ≥270(claim)

Ha:μ<270

H0:μ≤270(claim)

Ha:μ>270

H0:μ<270

Ha:μ≥270(claim)

(b) Find the standardized test statistic z, and its corresponding area.

(Round to two decimal places as needed.)

Find the P-value.

P-value=

(Round to three decimal places as needed.)

(C)Decide whether to reject or fail to reject the null hypothesis.

1.Reject H₀

2.Fail to reject H₀

Interpret your decision in the context of the original claim.

At the

11%

significance level, there

▼

1.is

2.is not

enough evidence to

▼

1.support

2.reject

the administrator's claim that the mean score for the state's eighth graders on the exam is more than

270.

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 + ...

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