Question

You have purchased an inexpensive USB oscilloscope (which measures and displays voltage waveforms). You wish to determine if the oscilloscope has an error bias; in other words, you wish to determine if the errors made by the oscilloscope have a population mean that is not equal to zero. So you use a very accurate voltmeter to find the measurement errors for 13 different measurements made by your USB oscilloscope. A data file containing these measurements is HTMean1.csvPreview the document . Do a statistical analysis on this data to determine if the oscilloscope has an error bias.

Answer 1

Complete Question

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Answer:

1

A

2

A

Step-by-step 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
`H_o : \mu = 0`

The alternative hypothesis is
`H_a : \mu \\e 0`

The sample size is n = 13

Here
`\mu` represents the true error bias (i.e population error bias)

Generally the sample error bias is mathematically represented as

`\= x = ( \sum x_i)/(n)`

=>
`\= x = ( -15.17 + 8.67 + (-13.74) + \cdots + (-14.77) )/(13)`

`\= x = -7.37`

Generally the standard deviation is mathematically represented as

`\sigma = \sqrt{(\sum (x_i - \= x )^2)/(n) }`

=>
`\sigma = \sqrt{( (-15.17-( -7.37) )^2 + (8.67 -( -7.37) )^2 + \cdots + (-14.77 -( -7.37) )^2 )/(13) }`

=>
`\sigma = √( 119.385)`

=>
`\sigma = 10.926`

Generally the test statistics is mathematically represented as

`t = (\= x - \mu )/((\sigma )/(√(n) ) )`

=>
`t = ( -7.37 - 0 )/((10.926)/(√(13) ) )`

=>
`t = -2.838`

Generally the p-value is mathematically represented as

`p-value = 2 P(t < -2.432)`

From the z-table
`P(t < -2.432) =  0.0075`

So
`p-value  =  2* 0.0075`

=>
`p-value  = 0.015`

So given that p-value is less than the
`\alpha = 0.05` then we reject the null hypothesis and conclude that the oscilloscope has an error bias