23.A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than14.8seconds. A random sample of24sedans has a mean minimum time to travel a quarter mile of15.5seconds and a standard deviation of2.08seconds. Atα=0.10is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and stateH0andHa. H0: muμ less than or equals≤ 14.814.8Ha: muμ greater than> 14.814.8(Type integers or decimals. Do not round.) The claim is thealternative hypothesis.(b) Use technology to find the P-value. Find the standardized test statistic, t. t=1.651.65(Round to two decimal places as needed.)Obtain the P-value. P=0.0560.056(Round to three decimal places as needed.)(c) Decide whether to reject or fail to reject the null hypothesis. ▼ RejectFail to rejectH0because the P-value▼ isis notgreater than a

Given: n= 24.0 ,x̄= 15.5 ,s= 2.08 µ= 14.8 ,significance level(∝)= 0.1 ,degree of freedom= 23.0define hypothesis;- Null Hypothesis, H0:µ= 14.8 Alternative hypothesis,H1:µ> 14.8 (right tailed test) Here n<30 so t-statistic test is used. Test Statistic. Under the H0, the test statistic is: t=(x̄-µ)/(s/√(n)) t=( 15.5 - 14.8 )/( 2.08 / √ 24.0 ) t= 1.6487=1.65 P-value: p=P(t> 1.6487 )=1-P(t< 1.6487 )=1- 0.9436 = 0.0564 conclusion: so here we can see that p-value < ∝ It is significant. Hence We reject null hypothesis(H0).because the P-value is not greater than α.

Answered: A consumer group claims that the mean…

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

23.

A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than

14.8

seconds. A random sample of

sedans has a mean minimum time to travel a quarter mile of

15.5

seconds and a standard deviation of

2.08

seconds. At

α=0.10

is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

(a) Identify the claim and state

and

Ha.

H0:	muμ less than or equals≤ 14.814.8
Ha:	muμ greater than> 14.814.8

(Type integers or decimals. Do not round.)

The claim is the

alternative

hypothesis.

(b) Use technology to find the P-value. Find the standardized test statistic, t.

t=1.651.65

(Round to two decimal places as needed.)

Obtain the P-value.

P=0.0560.056

(Round to three decimal places as needed.)

▼

Reject

Fail to reject

because the P-value

▼

is not

greater than a

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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