Question

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? 810     630     1203     607     578     612

What are the hypotheses

Identify the test statistic

Identify the P-value.

The critical value(s) is(are)

State the final conclusion that addressses the original claim

What do the results suggest about the child booster seats eeting the specific requirement?

Answer 1

Solution:

x	x2
810	656100
630	396900
1203	1447209
607	368449
578	334084
612	374544
x=4440	x2=3577286

The sample mean is

Mean = (x / n) )

=810+630+1203+607+578+612 /6

=4440/6

=740

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=3577286-(4440)²6 /5

=3577286-3285600 /5

=291686 /5

=58337.2

=241.531

Sample Standard deviation S=241.53

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 1000

H_a : < 1000

Test statistic = z

= ( - ) / / n

= (1000 -740) / 241.53 / 6

= −2.637

Test statistic = z = −2.637

The significance level is α=0.01, and the critical value for a left-tailed test is t_c​ =−3.365

P-value =0.0231

P-value ≥

0.0231 ≥ 0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that   the population mean μ is less than 1000,