# 12. Assume that a simple rando

12. Assume that a simple random sample has been selected from anormally distributed population and test the given claim. Identifythe null and alternative​ hypotheses, test​ statistic, P-value, andstate the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child boosterseats for cars. Listed below are results from those​ tests, withthe measurements given in hic​ (standard head injury condition​units). The safety requirement is that the hic measurement shouldbe less than 1000 hic. Use a 0.01 significance level to test theclaim that the sample is from a population with a mean less than1000 hic. Do the results suggest that all of the child boosterseats meet the specified​ requirement?

800,805,1326,644,621,592

What are the hypotheses?

a.Ho: µ > 1000 hic

H1: µ < 1000 hic

B.Ho: µ < 1000 hic

H1≥ 1000 hic

C.Ho: µ = 1000 hic

H1: µ ≥ 1000 hic

D. Ho: µ = 1000 hic

H1 µ < 1000 hic

Identify the test statistic.

T=

​(Round to three decimal places as​ needed.)

Identify the​ P-value.

The​ P-value is ___

​(Round to four decimal places as​ needed.)

State the final conclusion that addresses the originalclaim.

(Reject/fail to reject) H 0. There is (sufficient/insufficient)evidence to support the claim that the sample is from a populationwith a mean less than 1000 hic.

What do the results suggest about the child booster seatsmeeting the specified​ requirement?

A.There is not strong evidence that the mean is less than 1000​hic, and one of the booster seats has a measurement that is greaterthan 1000 hic.

B.The results are inconclusive regarding whether one of thebooster seats could have a measurement that is greater than 1000hic.

C.There is strong evidence that the mean is less than 1000​ hic,but one of the booster seats has a measurement that is greater than1000 hic.

D.The requirement is met since most sample measurements are lessthan 1000 hic

Sol:

Ho:

Ha:

alpha=0.01

use t.test function in R to get the t value and p value

Rcode is:

booster <- c(800,805,1326,644,621,592)t.test(booster,mu=1000,alternative = “less”,conf.level = 0.99)

output:

One Sample t-test

data: boostert = -1.8036, df = 5, p-value = 0.06558alternative hypothesis: true mean is less than 100099 percent confidence interval:-Inf 1174.871sample estimates:mean of x798

INTRePRETATION:

t=-1.804

p=0.0656

p>0.01

Fail to reject H0

State the final conclusion that addresses the originalclaim.

There is insufficient evidence to support the claim that thesample is from a population with a mean less than 1000 hic.

A.There is not strong evidence that the mean is less than 1000​hic,

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