2. The measured residual flame time, in seconds, for strips of treated children’s nightwear are given...

2. The measured residual flame time, in seconds, for strips of treated children’s nightwear are given in the following table.

9.85	9.93	9.75	9.77	9.67	9.87	9.67	9.94	9.85	9.75
9.83	9.92	9.74	9.99	9.88	9.95	9.95	9.92	9.93	9.89

Suppose a true average flame time of at most 9.75 seconds had been mandated. Does the data suggest that this condition has not been met? Carry out an appropriate test after first investigating the plausibility of assumptions that underlie your method of inference. Use the recommended sequence of steps and reach a conclusion using a significance level of 0.01:

Identify the parameter of interest and describe it in the context of the problem situation:

Determine the null value and state the null hypothesis:

State the appropriate alternative hypothesis:

Give the formula for the computed value of the test statistic (substituting the null value and the known values of any other parameters, but not those of any sample-based quantities):

Compute any necessary sample quantities, substitute into the formula for the test statistic value and compute that value:

Determine the P-value:

7. Compare the selected or specified significance level to the P-value to decide whether H₀ should be rejected, and state this conclusion in the problem context:

Expert Solution

2.
1.
the parameter of interest and describe it in the context of the problem situation:
T test for single mean with unknown population standard deviation
Given that,
population mean(u)=9.75
sample mean, x =9.8525
standard deviation, s =0.0965
number (n)=20
null, Ho: μ=9.75
alternate, H1: μ!=9.75
level of significance, α = 0.01
from standard normal table, two tailed t α/2 =2.861
since our test is two-tailed
reject Ho, if to < -2.861 OR if to > 2.861
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =9.8525-9.75/(0.0965/sqrt(20))
to =4.75
| to | =4.75
critical value
the value of |t α| with n-1 = 19 d.f is 2.861
we got |to| =4.75 & | t α | =2.861
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 4.7502 ) = 0.0001
hence value of p0.01 > 0.0001,here we reject Ho
ANSWERS
---------------
2.
null, Ho: μ=9.75
3.
alternate, H1: μ!=9.75
4.
we use test statistic (t) = x-u/(s.d/sqrt(n))
5.
test statistic: 4.75
critical value: -2.861 , 2.861
decision: reject Ho
6.
p-value: 0.0001
7.
p value is less than alpha value
we have enough evidence to support the claim that true average flame time of at most 9.75 seconds had been mandated

orchestra answered 1 year ago

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