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Answer:
There is enough statistical evidence to claim that the average length is not 10 cm.
Step-by-step explanation:
The claim that the average lenght is 10 cm, is the null hypothesis (has the "equal" sign). The claim that the average length is not 10 cm is the alternative hypothesis.
[tex]H_0:\mu=10\\\\H_a:\mu\neq 10[/tex]
The significance level is assumed to be 0.10.
The sample mean is 7 cm and the sample standard deviation is 1 cm.
The degrees of freedom are
[tex]df=n-1=100-1=99[/tex]
The t-statistic is:
[tex]t=\frac{M-\mu}{\sigma/\sqrt{n}} =\frac{7-10}{1/\sqrt{100}}=\frac{-3}{0.1}=-30[/tex]
The P-value of t=-30 is P=0.
This means there is almost no chance of getting this sample if the mean is really 10 cm.
There is enough statistical evidence to claim that the average length is not 10 cm.
The required average value is 10.
Critical value
The critical value in statistics is the measurement statisticians use to quantify the margin of error within a collection of data.
Given that,
[tex]H_0:\mu=10\\H_1:\mu \ne10 \ for\ 0.05\\critical\ value=\pm1.96\\z=\frac{7-10}{1}\\ z=-3[/tex]
Since [tex]z[/tex] is greater than the critical value, then we reject [tex]H_0[/tex] and say that there are such evidence to reject that average is 10.
Learn more about the topic Critical value:
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