Apply the test in Example 2 to the following data (x = disulfide content of a certain

What would change in Example 1. had we observed only 5 positive values? Only 4?

Does a process of producing plastic pipes of length \(\mu=2\) meters need adjustment if in a sample. 4 pipes have the exact length and 15 are shorter and 3 longer than 2 meters? (Use the normal approximation of the binomial distribution.) Text Transcription: mu = 2

Do the computations in Prob. 2 without the use of the DeMoivre-Laplace limit theorem (in Sec. 24.8).

Test whether a thermostatic switch is properly set to \(20^{\circ} \mathrm{C}\) against the alternative that its setting is too low. Use a sample of 9 values, 8 of which are less than \(20^{\circ} \mathrm{C}\) and 1 is greater than \(20^{\circ} \mathrm{C}\). Text Transcription: 20^{circ} C

Are air filters of type A better than type B filters if in 10 trials. A gave cleaner air than B in 7 cases, B gave cleaner air than A in 1 case, whereas in 2 of the trials the results for A and B were practically the same?

In a clinical experiment, each of 10 patients were given two different sedatives A and B. The following table shows the effect (increase of sleeping time. measured in hours). Using the sign test. find out whether the difference is significant.

Assuming that the populations corresponding to the samples in Prob. 6 are normal, apply a suitable test for the normal distribution.

Thirty new employees were grouped into 15 pairs of similar intelligence and experience and were then instructed in data processing by an old method (A) applied to one (randomly selected) person of each pair. and by a new presumably better method (B) applied to the other person of each pair. Test for equality of methods against the alternative that (B) is better than (A), using the following scores obtained after the end of the training period.

Assuming normality. solve Prob. 8 by a suitable test from Sec. 25.4.

Set up a sign test for the Iower quartile \(q_{25}\) (defined by the condition \(\left.F\left(q_{25}\right)=0.25\right)\). Text Transcription: q_25 F(q_25) = 0.25)

How would you proceed in the sign test if the hypothesis is \(\tilde{\mu}=\tilde{\mu}_{0}\) (any number) instead of \(\tilde{\mu}=0^{\prime}\)? Text Transcription: tilde{mu} = tilde{mu}_{0} tilde{mu} = 0^{prime}

Check the table in Example 2 of the text.

Apply the test in Example 2 to the following data (x = disulfide content of a certain type of wool, measured in percent of the content in unreduced fibers; y = saturation water content of the wool, measured in percent). Test for no trend against negative trend.

Test the hypothesis that for a certain type of voltmeter, readings are independent of temperature \(T\left[{ }^{\circ} \mathrm{C}\right]\) against the alternative that they tend to increase with T. Use a sample of values obtained by applying a constant voltage: Text Transcription: T [^{circ} C]

In a swine-feeding experiment. the following gains in weight [kg] of 10 animals (ordered according to increasing amounts of food given per day) were recorded: 20 17 19 18 23 16 25 28 24 22. Test for no trend against positive trend.

Apply the test explained in Example 2 to the following data (x = diastolic blood pressure [mm Hg]. y = weight of heart [in grams] of 10 patients who died of cerebral hemorrhage).

Does an increase in temperature cause an increase of the yield of a chemical reaction from which the following sample was taken?

Does the amount of fertilizer increase the yield of wheat X [kg/plot]? Use a sample of values ordered according to increasing amounts of fertilizer: 41.4 43.3 39.6 43.0 44.1 45.6 44.5 46.7.