Question

Question Help Assume that a simple random sample has been selected from a normaly distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic 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 requirements 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 ched booster seats meet the specified requirement? 685 648 1097 586 512 432 What are the hypotheses? O A. Ho - 1000 hic OBH 1000 hic H: 1000 hic H, H = 100 g OC. Ho <1000 hic OD. My 1000 H21000 NG H<1000 e Identify the test statistic (Round to three decimal places as needed)

Answer 1

Ans : Given data are

685,648,1097,586,512,432,

sample mean

$\bar{X} =\frac{\sum x}{n}$

$\bar{X}$ =660

s1 = (E(Xi – X)^2 n 1

S1 = 232.85

here claim that the sample is from population with a mean less that 1000 hic

the Hypothesis :

H₀ : $\mu$ = 1000 hic

H₁ : $\mu$ < 1000 hic

Here we use left tailed t test for population mean

Test Statistics :

(X t μο) (s/νη)

t = (660 - 1000)/(232.85/$\small \sqrt{6}$ )

t= -3.5766

The Test statistic is

t = -3.577

under h0 t follows t-distribution with n-1 degrees of freedom

df = 6-1 = 5

p value :

given significance level is 0.01

p - value =0 .007963

Critical region :

If p-value < $\alpha$ = 0.01 then we reject H0 at 0.01 significance level

Since here p -value = 0.007963 < $\alpha$ = 0.01 Then we reject H0 at 0.01 level of significance

The final Conclusion that addresses the original claim :

Reject H0 , there is sufficient evidence to support the claim that the sample is from a population with a mean less than 1000 hic

What do the result suggest about the child booster seats meeting the specified requirement

Ans : C , There is strong evidence that the mean is less than 1000 hic but one of the booster has a measurement that is greater than 1000 hic