Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ≥8300; α=0.01 Sample statistics: x=8100, s=430, n=24 What are the null and alternative hypotheses? A. H0: μ≥8300 Ha: μ<8300 B. H0: μ≠8300 Ha: μ=8300 C. H0: μ=8300 Ha: μ≠8300 D. H0: μ≤8300 Ha: μ>8300 What is the value of the standardized test statistic? The standardized test statistic is nothing. (Round to two decimal places as needed.) What is the P-value? P=nothing (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. A. Fail to reject H0. At the 1% level of significance, there is not enough evidence to reject the claim. B. Reject H0. At the 1% level of significance, there is not enough evidence to reject the claim. C. Fail to reject H0. At the 1% level of significance, there is enough evidence to reject the claim. D. Reject H0. At the 1% level of significance, there is enough evidence to reject the claim.

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

Use a t-test to test the claim about the population mean

at the given level of significance

using the given sample statistics. Assume the population is normally distributed.

Claim:

μ≥8300;

α=0.01

Sample statistics:

x=8100,

s=430,

n=24

What are the null and alternative hypotheses?

H0:

μ≥8300

Ha:

μ<8300

H0:

μ≠8300

Ha:

μ=8300

H0:

μ=8300

Ha:

μ≠8300

H0:

μ≤8300

Ha:

μ>8300

What is the value of the standardized test statistic?

The standardized test statistic is

nothing.

(Round to two decimal places as needed.)

What is the P-value?

P=nothing

(Round to three decimal places as needed.)

Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

Fail to reject

H0.

At the

level of significance, there

is not

enough evidence to reject the claim.

Reject

H0.

At the

level of significance, there

is not

enough evidence to reject the claim.

Fail to reject

H0.

At the

level of significance, there

enough evidence to reject the claim.

Reject

H0.

At the

level of significance, there

enough evidence to reject the claim.

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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