Complete Question
Each of the following hypothetical data set represents some repeated weighing of a standard weight that is known to have a mass of 100 g. Assume that the readings are a random sample from a population that follows the normal curve. We perform a t-test to see whether the scale is properly calibrated. Find the corresponding P-value for this test..
The data in grams are
100.02 , 99.98 , 100.03
Answer:
The p-value is [tex]p-value =0.5798[/tex]
Step-by-step explanation:
Generally the sample mean of the given data is mathematically represented as
[tex]\= x = \frac{100.02 + 99.98 + 100.03 }{3}[/tex]
[tex]\= x =100.03 \ g[/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{\sum [x_i - \= x]^2 }{n-1} }[/tex]
=> [tex]s = \sqrt{\frac{[ 100.02 - 100.01]^2+ [ 99.98 - 100.01]^2+[ 100.03 - 100.01]^2 }{3-1} }[/tex]
=> [tex]s = 0.02645[/tex]
The null hypothesis is [tex]H_o : \mu = 100[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 100[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 3 - 1[/tex]
=> [tex]df = 2[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 100.01 - 100 }{\frac{0.02645}{\sqrt{3} } }[/tex]
=> [tex]t = 0.655[/tex]
From the t distribution table the probability corresponding to the t to the right of the bell curve at a degree of freedom of [tex]df = 2[/tex]
[tex]P( T > 0.655 ) = 0.2899[/tex]
Generally the p-value for this two tailed test is mathematically represented as
[tex]p-value = 2 * P(T > 0.655)[/tex]
=> [tex]p-value = 2 * 0.2899[/tex]
=> [tex]p-value =0.5798[/tex]
