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In 2001, the polls found that 81% of American adults believed that there was a conspiracy in the death of President Kennedy. Assume a recent poll asked 1740 American adults if they believe there was a conspiracy in the assassination and it found that 1374 believe there was a conspiracy. Does the data show that the proportion of Americans who believe in this conspiracy is now lower? Test at the 5% level.P: PARAMETER     What is the correct parameter symbol for this problem?          What is the wording of the parameter in the context of this problem?     H: HYPOTHESES     Fill in the correct null and alternative hypotheses:     𝐻0:      𝐻𝐴: A: ASSUMPTIONS     Since information was collected from each object, what conditions do we need to check?     Check all that apply.     𝑛(𝑝̂)≥10𝑁≥20𝑛𝑛𝑝≥10𝑛(1-𝑝)≥10𝑛(1-𝑝̂)≥10σσ is known.𝑛≥30 or normal population.σσ is unknown.     Check those assumptions:          1. 𝑛𝑝 = which is           2. 𝑛(1-𝑝) = which is           3. 𝑁 = which is               If no N is given in the problem, use 1000000N: NAME THE PROCEDURE     The conditions are met to use a .T: TEST STATISTIC     The symbol and value of the random variable on this problem are as follows:     Leave this answer as a fraction.     =      The formula set up of the test statistic is as follows.:       (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / )       Final answer for the test statistic from technology.     Round to 2 decimal places:     z = O: OBTAIN THE P-VALUE     Report to 4 decimal places.     It is possible when rounded that a p-value is 0.0000     P-value = M: MAKE A DECISION     Since the p-value , we .S: STATE A CONCLUSION    There significant evidence to conclude

Question

In 2001, the polls found that 81% of American adults believed that there was a conspiracy in the death of President Kennedy. Assume a recent poll asked 1740 American adults if they believe there was a conspiracy in the assassination and it found that 1374 believe there was a conspiracy. Does the data show that the proportion of Americans who believe in this conspiracy is now lower? Test at the 5% level.P: PARAMETER     What is the correct parameter symbol for this problem?          What is the wording of the parameter in the context of this problem?     H: HYPOTHESES     Fill in the correct null and alternative hypotheses:     𝐻0:      𝐻𝐴: A: ASSUMPTIONS     Since information was collected from each object, what conditions do we need to check?     Check all that apply.     𝑛(𝑝̂)≥10𝑁≥20𝑛𝑛𝑝≥10𝑛(1-𝑝)≥10𝑛(1-𝑝̂)≥10σσ is known.𝑛≥30 or normal population.σσ is unknown.     Check those assumptions:          1. 𝑛𝑝 = which is           2. 𝑛(1-𝑝) = which is           3. 𝑁 = which is               If no N is given in the problem, use 1000000N: NAME THE PROCEDURE     The conditions are met to use a .T: TEST STATISTIC     The symbol and value of the random variable on this problem are as follows:     Leave this answer as a fraction.     =      The formula set up of the test statistic is as follows.:       (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / )       Final answer for the test statistic from technology.     Round to 2 decimal places:     z = O: OBTAIN THE P-VALUE     Report to 4 decimal places.     It is possible when rounded that a p-value is 0.0000     P-value = M: MAKE A DECISION     Since the p-value , we .S: STATE A CONCLUSION    There significant evidence to conclude

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Solution

P: PARAMETER

  • The correct parameter symbol for this problem is p p .
  • The wording of the parameter in the context of this problem is: the proportion of American adults who believe there was a conspiracy in the assassination of President Kennedy.

H: HYPOTHESES

  • Null hypothesis (H0 H_0 ): p=0.81 p = 0.81
  • Alternative hypothesis (HA H_A ): p<0.81 p < 0.81

A: ASSUMPTIONS

  • Since information was collected from each object, the conditions we need to check are:
    • np^10 n \hat{p} \geq 10
    • n(1p^)10 n(1 - \hat{p}) \geq 10
    • N20n N \geq 20n
  • Check those assumptions:
    1. np^=1740×13741740=1374 n \hat{p} = 1740 \times \frac{1374}{1740} = 1374 , which is greater than 10.
    2. n(1p^)=1740×(113741740)=366 n(1 - \hat{p}) = 1740 \times (1 - \frac{1374}{1740}) = 366 , which is greater than 10.
    3. N=1000000 N = 1000000 , which is greater than 20×1740=34800 20 \times 1740 = 34800 .

N: NAME THE PROCEDURE

  • The conditions are met to use a one-sample z-test for proportions.

T: TEST STATISTIC

  • The symbol and value of the random variable on this problem are as follows:
    • p^=13741740=0.79 \hat{p} = \frac{1374}{1740} = 0.79
  • The formula setup of the test statistic is as follows: z=p^pp(1p)n=0.790.810.81×(10.81)1740 z = \frac{\hat{p} - p}{\sqrt{\frac{p(1 - p)}{n}}} = \frac{0.79 - 0.81}{\sqrt{\frac{0.81 \times (1 - 0.81)}{1740}}}
  • Final answer for the test statistic from technology:
    • z=1.48 z = -1.48 (rounded to 2 decimal places)

O: OBTAIN THE P-VALUE

  • Report to 4 decimal places:
    • P-value = 0.0694

M: MAKE A DECISION

  • Since the p-value (0.0694) is greater than the significance level (0.05), we fail to reject the null hypothesis.

S: STATE A CONCLUSION

  • There is not significant evidence to conclude that the proportion of Americans who believe in the conspiracy is now lower than 81%.

This problem has been solved

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