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In: Statistics and Probability

Assume that a simple random sample has been selected from a normally distributed population and test...

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 0.05 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? 669 635 1144 661 600 749

Solutions

Expert Solution

H0: Null Hypothesis: 1000 ( The sample is not from a population with a mean less than 1000 hic.)

HA: Alternative Hypothesis: 1000 ( The sample is from a population with a mean less than 1000 hic.) (Claim)

From the given data, the following statistics are calculated:

n = 6

= 743

s = 202.5586

= 05

df = 6 - 1 = 5

From Table, critical value of t = - 2.015

Test Statistic is given by:

Sonce calculated value of t = - 3.108 is less than critical value of t = - 2.015, the difference is sigificant. Reject null hypothesis.

Conclusion:The data support the claim that the sample is from a population with a mean less than 1000 hic.

The results suggest that all of the child booster seats meet the specified​ requirement with 95% confidence level.

orchestra answered 1 year ago
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