Question

# safety administration conducted crash tests of child booster seats for cars. Listed below are results from...

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 is that the hic measurements 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? 622 617 1189 597 543 470

To test $H_0:\mu = 1000$ against $H_1:\mu < 1000$

Here

sample mean $\bar{x} = 673$

sample standard deviation $s = 259$

and sample size $n = 6$

The test statistic can be written as

$t = \frac{\sqrt{n}(\bar{x} - 1000)}{s}$ which under H0 follows a t distribution with n-1 df.

We reject H0 at 0.05 significance level if P-value < 0.05

Now,

The value of the test statistic = $t_{obs} = -3.09260$

and P-value = $P(t_{n-1}

Since p-value <0.05, so we reject H0 at 0.05 significance level and we can conclude that population mean is significantly less than 1000 hic.

#### Earn Coins

Coins can be redeemed for fabulous gifts.