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Chapter 8: Q2E (page 325)

For the following pairs of assertions, indicate which with our rules for setting up hypotheses and why (the subscripts 1 and 2 differentiate between quantities for two different populations or samples):

a. H0: 碌= 100, Ha: 碌 > 100

b.H0: 蟽= 20, Ha: \(\sigma \le 20\)

c.H0: p鈮� .25, Ha: p= .25

d.H0: 碌1 - 碌2 = 25, Ha: 碌1 - 碌2 > 100

e.H0: \(S_1^2 = S_2^2\) , Ha: \(S_1^2 \ne S_2^2\)

f.H0: 碌= 120, Ha: 碌= 150

g.H0: 蟽1,/蟽2 =1,Ha: 蟽1,/ 蟽2 鈮�1

h.H0p1 鈥� p2 = -.1, Ha: p1 鈥� p2 < -.1

Short Answer

Expert verified

a)Yes , b) No, c) No, d) No, e) No, f) No, g) Yes, h) Yes.

Step by step solution

01

Step 1:Statistical hypothesis.

A statistical hypothesis, or just hypothesis, is a claim or assertion either about the value of a single parameter (population characteristic or characteristic of a probability distribution), about the values of several parameters, or about the form of an entire

probability distribution.

02

Step 2:Solution for part a), b) and c).

a)This is a valid hypotheses. It complies with the rules.

b)This is not a valid hypotheses. Both \({H_0}\) and \({H_a}\) contain equality \((\sigma = 20)\), therefore it does not comply with the rules.

c)The hypotheses \({H_0}\) should be the equality claim, and in this case the hypotheses \({H_a}\) contains the equality claim, therefore it does not comply with the rules.

03

Step 3:Solution for part d) and e).

d)Both hypotheses \({H_0}\) and \({H_a}\) should contain same values in order for the hypotheses to comply. First asserted value of \({\mu _1} - {\mu _2}\) is \(25\), whereas the other \(100\), therefore it does not comply with the rules.

e)The statistics can not belong to the test hypothesis. Therefore it does not comply with the rules because \({S_i}\) are statistics.

04

 Step 4:Solution for part  f) ,g) and h).

f)It is not allowed for both hypotheses to have an equality claims, therefore it does not comply with the rules. (it is allowed in some more complicated hypothesis testing).

g)This is a valid hypotheses. It complies with the rules.

h)This is a valid hypotheses. It complies with the rules.

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Most popular questions from this chapter

In Problems \(11 - 14\) verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.

\(y'' + y = tanx; y = - (cosx) ln(secx + tanx)\).

The relative conductivity of a semiconductor device is determined by the amount of impurity 鈥渄oped鈥� into the device during its manufacture. A silicon diode to be used for a specific purpose requires an average cut-on voltage of \(.60V\), and if this is not achieved, the amount of impurity must be adjusted. A sample of diodes was selected and the cut-on voltage was determined. The accompanying SAS output resulted from a request to test the appropriate hypotheses.

(Note: SAS explicitly tests \({H_0}:\mu = 0\), so to test \({H_0}:\mu = .60\), the null value \(.60\) must be subtracted from each \({x_i}\); the reported mean is then the average of the \(({x_i} - .60)\) values. Also, SAS鈥檚 P-value is always for a two-tailed test.) What would be concluded for a significance level of \(.01\)? \(.05\)? \(.10\)?

For each of the following assertions, state whether it is a legitimate statistical hypothesis and why:

\(\begin{array}{l}{\rm{a}}{\rm{. H: \sigma > 100}}\\{\rm{c}}{\rm{. H: s }} \le {\rm{.20}}\\{\rm{e}}{\rm{. H:}}\overline {{\rm{ X}}} {\rm{ - }}\overline {\rm{Y}} {\rm{ = 5}}\end{array}\) \(\begin{array}{l}{\rm{b}}{\rm{. H: }}\widetilde {\rm{x}}{\rm{ = 45}}\\{\rm{d}}{\rm{. H: }}{{\rm{\sigma }}_{\rm{1}}}{\rm{/}}{{\rm{\sigma }}_{\rm{2}}}{\rm{ < 1}}\end{array}\)

\({\rm{f}}{\rm{. H: \lambda }} \le {\rm{.01}}\), where \({\rm{\lambda }}\) is the parameter of an exponential distribution used to model component lifetime

A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design.

a.Define the parameter of interest and state the relevant hypotheses.

b.Suppose braking distance for the new system is normally distributed with 蟽= 10. Let \(\overline X \) denote the sample average braking distance for a random sample of 36 observations. Which values of \(\overline x \) are more contradictory to H0 than 117.2, what is the P-value in this case, and what conclusion is appropriate if 伪 = .10?

c.What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used?

In Problems \(31 - 34\) find values of m so that the function \(y = m{e^{mx}}\) is a solution of the given differential equation.

\(5y' = 2y\)
See all solutions

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