Assume that a simple random sample has been selected from a

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 0.050.05 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? 666 593 1047 555 495 586

Solution

Sample data is 666 593 1047 555 495 586

Find sample mean and std deviation

n =6

Mean = 657

std dev =198.98

Std error = 198.98/rt 6 = 81.233

H0: mu = 1000

Ha: mu <1000

Left tailed test

Test statistic t = \\frac{1000-657}{198.98}

= 1.724

Alpha = 0.05

p value = .072655.

The result is not significant at p < .05.

Hence accept null hypothesis and there is evidence that the results suggest that all of the child booster seats meet the specified requirement