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

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 $H_a : \mu \ne 0$

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

$\= x = \frac{ \sum x_i}{n}$

=> $\= x = \frac{ -15.17 + 8.67 + (-13.74) + \cdots + (-14.77) }{13}$

$\= x = -7.37$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x )^2}{n} }$

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

=> $\sigma = \sqrt{ 119.385}$

=> $\sigma = 10.926$

Generally the test statistics is mathematically represented as

$t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }$

=> $t = \frac{ -7.37 - 0 }{\frac{10.926}{\sqrt{13} } }$

=> $t = -2.838$

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