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? 823     642     1341     672     585     461

What are the​ hypotheses?

A. Upper H 0​: muequals1000 hic Upper H 1​: muless than1000 hic

B. Upper H 0​: muequals1000 hic Upper H 1​: mugreater than or equals1000 hic

C. Upper H 0​: muless than1000 hic Upper H 1​: mugreater than or equals1000 hic

D. Upper H 0​: mugreater than1000 hic Upper H 1​: muless than1000 hic

Identify the test statistic. ​(Round to three decimal places as​ needed.)

Identify the​ P-value. ​(Round to four decimal places as​ needed.)

State the final conclusion that addresses the original claim. Fail to reject Reject Upper H 0. There is insufficient sufficient evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

Answer 1

(1)

Ho: = 1000

Ha: < 1000 (claim)

A. Upper H 0​: muequals1000 hic Upper H 1​: muless than1000 hic

(2) Test statistics

Assuming that the data is normally distributed and also aspopulation sd is not given, we will calculate t stat.

sample mean = sum of all terms / no of terms = 4524 / 6 = 754

sample sd = s

data	data-mean	(data - mean)2
823	69	4761
642	-112	12544
1341	587	344569
672	-82	6724
585	-169	28561
461	-293	85849

(3) p value using excel formula = TDIST ( 1.939, 5,1) = 0.0551

(4) As p value (0.0551) is  greater than level of significance (0.01) we fail to reject the Null hypothesis.

Fail to reject Reject H 0. There is insufficient evidence to support the claim that the sample is from a population with a mean less than 1000 hic.