Complete Question
The complete question is shown on the first uploaded image
Answer:
1
A
2
A
Explanation:
From the question the data given for Error (mV) is -15
-15.17
8.67
-13.74
-20.69
-6.96
-1.36
-2.96
-9.26
3.11
-14.12
6.39
-14.77
Generally
The null hypothesis is [tex]H_o : \mu = 0[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 0[/tex]
The sample size is n = 13
Here [tex]\mu[/tex] represents the true error bias (i.e population error bias)
Generally the sample error bias is mathematically represented as
[tex]\= x = \frac{ \sum x_i}{n}[/tex]
=> [tex]\= x = \frac{ -15.17 + 8.67 + (-13.74) + \cdots + (-14.77) }{13}[/tex]
[tex]\= x = -7.37[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x )^2}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ (-15.17-( -7.37) )^2 + (8.67 -( -7.37) )^2 + \cdots + (-14.77 -( -7.37) )^2 }{13} }[/tex]
=> [tex]\sigma = \sqrt{ 119.385}[/tex]
=> [tex]\sigma = 10.926[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ -7.37 - 0 }{\frac{10.926}{\sqrt{13} } }[/tex]
=> [tex]t = -2.838[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P(t < -2.432)[/tex]
From the z-table [tex]P(t < -2.432) = 0.0075 [/tex]
So [tex]p-value = 2* 0.0075 [/tex]
=> [tex]p-value = 0.015 [/tex]
So given that p-value is less than the [tex] \alpha = 0.05[/tex] then we reject the null hypothesis and conclude that the oscilloscope has an error bias
