In a nationally representative sample of 1,668 adult Americans, 930 indicated that they had checked their credit score within the last 12 months. Suppose of the 930 people that had checked their credit report within the last 12 months, 37% had done so as part of their regular financial planning. Does this provide convincing evidence that more than one-third of adult Americans who have checked their credit scores within the past 12 months did so as part of regular financial planning

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05-04-2021
Mathematics

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In a nationally representative sample of 1,668 adult Americans, 930 indicated that they had checked their credit score within the last 12 months. Suppose of the 930 people that had checked their credit report within the last 12 months, 37% had done so as part of their regular financial planning. Does this provide convincing evidence that more than one-third of adult Americans who have checked their credit scores within the past 12 months did so as part of regular financial planning

Sagot :

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AbsorbingMan AbsorbingMan · Answer 1 · 2021-04-07T09:18:13-04:00

Solution :

The one sample proportion summary hypothesis test is :

p : proportion of successes

[tex]$H_0: p = 0.33 $[/tex]

[tex]$H_a : p > 0.33$[/tex]

The hypothesis test result by using the statistical software is :

Total = 930

Sample proportion = 0.37

Standard error = 0.0157

Z-stat = 1.697

P- value = 0.0448

Therefore, the hypothesis [tex]$H_0:p = \frac{1}{3} \text{ versus}\ H_a: p > \frac{1}{3}$[/tex] is correct.

And conclusion : Fail to reject [tex]$H_0$[/tex]. As we do not have any convincing evidence that more than one-third of adult Americans who have checked their credit scores within the past 12 months did so as part of regular financial planning.

Sagot :

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