Before endorsing a candidate for political office, a newspaper editor surveys 20

Question

Before endorsing a candidate for political office, a newspaper editor surveys 200 randomly selected readers and finds that 140 favor the candidate in question. At the 0.05 level of significance, test the editor's claim that the candidate is favored by more than two-thirds of the readers. The correct statement for the claim in this test is:

2) The critical value for this test is

-1.96

1.645

1.96

-1.645

3) The test statistic for this test is

1.00

-1.00

5.42

-5.42

4) The conclusion is

Fail to reject Ho says that there is insufficient evidence to support the claim that the modified components have a longer mean time between failures.

Fail to reject Ho which says there is insufficient evidence to warrent rejection of the claim that the modified component have a longer mean time between failures.

Reject Ho which says there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

Reject Ho which says there is sufficient evidence to warrent rejection of the claim that the modified components have a longer mean time between failures

Explanation / Answer

1.

Claims go to the alternative hypothesis, and they never contain = signs, so

OPTION B: p > 2/3 [ANSWER]

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2.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.666666667
Ha:   p   >   0.666666667

As this is a right tailed 0.05 level test,

zcrit = 1.645 [ANSWER, B]

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3.

As we see, the hypothesized po =   0.666666667      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.7      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.033333333      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1   [ANSWER, A]

********************

4.  
          
As z < 1.645, we fail to reject Ho. Hence,

OPTION B: Fail to reject Ho which says there is insufficient evidence to warrent rejection of the claim that the modified component have a longer mean time between failures. [ANSWER, B]

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