Answered: A recent broadcast of a television show…

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 recent broadcast of a television show had a 10
share, meaning that among 6000 monitored households with TV sets in use, 10% of them were tuned to this program. Use a 0.01 significance level to test the claim of an advertiser that among the households with TV sets in use, less than 15%
were tuned into the program. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

Identify the null and alternative hypotheses. Choose the correct answer below.

H0:p=0.15

H1: p>0.15

H0:p=0.15

H1:p≠0.150.15

H0:p=0.85

H1:p<0.850.85

H0:p=0.15

H1:p<0.150.15

H0:p=0.85

H1:p>0.85

H0:p=0.85

H1:p≠0.85

Should cover everything example does BELOW

A recent broadcast of a television show had a 20
share, meaning that among 5500
monitored households with TV sets in use,

20% of them were tuned to this program. Use a 0.01 significance level to test the claim of an advertiser that among the households with TV sets in use, less than

30% were tuned into the program. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

Identify the null and alternative hypotheses.

The null hypothesis,

H0, is a statement that the value of a population parameter is equal to some claimed value. The alternative hypothesis,

H1, is a statement that the parameter has a value that somehow differs from the null hypothesis.

Identify the claim about the population proportion p. This is the hypothesis that will be tested.

p<0.30 he symbolic form that must be true when the claim is false is P≥0.30 Therefore, H0 is

P=0.30 and H1 is p<0.30

Identify the level of significance

alphaα.

alphaαequals=0.01

Identify the test statistic.

Solve for the test statistic using the formula below, where n is the sample size, p is the population proportion based on the claim, q is equal to

(1minus−p),

and

ModifyingAbove p with caretpequals=StartFraction number of successes x Over n EndFractionnumber of successes xn

is the sample proportion.

zequals=StartFraction ModifyingAbove p with caret minus p Over StartRoot StartFraction pq Over n EndFraction EndRoot EndFractionp−ppqn

Let

pequals=0.300.30,

the population proportion given in the claim.

Solve for q. Substitute the value of

pequals=0.300.30

into the formula below.

qequals=1minus−p

qequals=1minus−0.300.30

qequals=0.700.70

The sample proportion

ModifyingAbove p with caretp

is equal to

0.200.20,

because

2020%

55005500

monitored households with TV sets in use were tuned to this program.

Calculate the test statistic. Substitute

pequals=0.300.30,

qequals=0.700.70,

ModifyingAbove p with caretpequals=0.200.20,

and

nequals=55005500

into the formula below and simplify, rounding to two decimal places.

zz	equals=	StartFraction ModifyingAbove p with caret minus p Over StartRoot StartFraction pq Over n EndFraction EndRoot EndFractionp−ppqn
	equals=	StartFraction 0.20 minus 0.30 Over StartRoot StartFraction left parenthesis 0.30 right parenthesis left parenthesis 0.70 right parenthesis Over 5500 EndFraction EndRoot EndFraction0.20−0.30(0.30)(0.70)5500
	equals=	negative 16.18−16.18

Identify the P-value.

The P-value is the probability of getting a test statistic at least as extreme as the value representing the sample data.

Determine if the test is left-tailed, right-tailed, or two-tailed. If the alternative hypothesis has the

not equals≠

symbol, then the test is two-tailed. If the alternative hypothesis has the

less than<

symbol, then the test is left-tailed. If the alternative hypothesis has the

greater than>

symbol, then the test is right-tailed.

The test is left-tailed.

The area of the P-value is determined by the type of test being conducted. In a left-tailed test, the P-value is equal to the area to the left of the test statistic z. In a right-tailed test, the P-value is equal to the area to the right of the test statistic z. In a two-tailed test, the P-value is equal to twice the extreme region bounded by the test statistic z.

While either technology or a standard normal distribution table could be used to find the P-value, for the purposes of this explanation, use technology. Recall that

zequals=negative 16.18−16.18.

Find the P-value for the left-tailed test, rounding to four decimal places.

P-valueequals=0.0000

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

If the P-value is less than or equal to the level of significance

alphaα,

reject

H0,

and conclude that there is sufficient evidence to warrant rejection of the claim. Otherwise, fail to reject

H0,

and conclude that there is insufficient evidence to warrant the rejection of the claim.

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.

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