Question

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

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

671, 654, 1252, 617, 599, 443

What are the​ hypotheses?

A.Upper H 0​:mu less than1000hic

Upper H 1​:mu greater than or equals1000hic

B.Upper H 0​:mu equals1000 hic

Upper H 1​:mu less than1000hic

C.Upper H 0​:mu greater than1000 hic

Upper H 1​:mu less than1000 hic

D.Upper H 0​:mu equals1000hic

Upper H 1​: mu greater than or equals1000 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 original claim.

▼

Fail to reject or Reject? Upper H 0.

There is

▼

insufficient or sufficient? evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

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

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

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

C.The requirement is met since most sample measurements are less than 1000 hic.

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

Answer 1

Here claim is that the hic measurement should be less than 1000 hic

So hypothesis is

B.Upper H 0​:mu equals1000 hic

Upper H 1​:mu less than1000hic

For given data mean=AVERAGE(E9:E14)=706 and sd=STDEV(E9:E14)=279.494

Test statistics is

P value is TDIST(2.58,5,1)=0.0247>alpha=0.01

As P value is greater than alpha we fail to reject the null hypothesis

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

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