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NemiM [27]
3 years ago
12

The calibration of a scale is to be checked by weighing a 13 kg test specimen 25 times. Suppose that the results of different we

ighings are independent of one another and that the weight on each trial is normally distributed with Sigma = 0.200 kg. Let µ denote the true average weight reading on the scale.
Required:
a. What hypotheses should be tested?
b. With the sample mean itself as the test statistic, what is the P-value?
Mathematics
1 answer:
Natali5045456 [20]3 years ago
3 0

Solution :

a).

Given : Number of times, n = 25

            Sigma, σ = 0.200 kg

            Weight, μ = 13 kg

Therefore the hypothesis should be tested are :

$H_0 : \mu = 13 $

$H_a : \mu \neq 13$

b). When the value of $\overline x = 12.84$

 Test statics :

   $Z=\frac{(\overline x - \mu)}{\frac{\sigma}{\sqrt n}} $

  $Z=\frac{(14.82-13)}{\frac{0.2}{\sqrt {25}}} $

          $=\frac{1.82}{0.04}$

          = 45.5  

P-value = 2 x P(Z > 45.5)

            = 2 x 1 -P (Z < 45.5) = 0

Reject the null hypothesis if P value  < α = 0.01 level of significance.

So reject the null hypothesis.

Therefore, we conclude that the true mean measured weight differs from 13 kg.

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I think your question missed key information, allow me to add in and hope it will fit the orginal one.

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