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? 755 735 1373 680 625 524

Question

contestada

Respuesta :

MrSmoot MrSmoot · Answer 1 · 2019-04-22T19:13:17+02:00

Answer:

Yes, the results show the child booster seat meets the specified requirement

Step-by-step explanation:

We will conduct a one sample hypothesis test. Our sample size of 6, so we will use t-distribution to find our critical values.

This is a left tailed test, with degrees of freedom being 5.

First we need the sample mean and standard deviation. See first attached photo for these calculations...

See attached photo 2 for the hypothesis test

Answer Link

AFOKE88 AFOKE88 · Answer 2 · 2022-04-26T15:52:09+02:00

We fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

Let us first define the hypotheses;

Null hypothesis: H₀: µ ≥ 1000

Alternative hypothesis: Hₐ: µ < 1000 (claim)

The given 6 results are; 755, 735, 1373, 680, 625, 524

Mean is;

x' = (755 + 735 + 1373 + 680 + 625 + 524)/6

x' = 782

From online standard deviation calculator, the standard deviation is;

s = 301.276

Formula for test statistic is;

z = (x' - µ)/(s/√n)

z = (782 - 1000)/(301.276/√6)

z = -1.77

From online p-value from z-score calculator using 0.01 as significance level gives; p = 0.038364

Thus, we fail to reject the null Hypothesis and conclude that there is insufficient evidence to support the claim.

Read more about Hypothesis Conclusion at; https://brainly.com/question/15980493